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BY WILLIAM H. REUCK. 


aas 


Principat or Warp Scuoon No. 7, anp Proressor or MATHEMATICS © 


IN THE Matz Norma. Scuoor or New York. 


NEW YORK: 


A. S8. BARNES & Co., 111 & 113 WILLIAM STREET, 
(CORNER OF JOHN STREET.) 


1866. 


ENTERED according to Act of Congress, in the year One Thousand Eight 
Hundred and Fifty-four, by WILLIAM H. REUCK, in the Clerk’s 
Office of the District Court of the United States, for the Southera District 
of New York. 


MATHEMATICS LIBRAK? 


PREFACE. 


Ir is with much diffidence that the author presents 
this volume to the public, particularly when there are 
already many books on the same subject, written by 
persons of superior attainments and practical ability, 
sufficient to cover the whole ground of arithmetic. But 
within the last few years the grade of common schoo, 
education has advanced so rapidly, and the theoretical 
parts of arithmetic are so thoroughly taught, that a book 
which should contain a complete treatise of theory and 
practice, would constitute a work almost too lumber- 
some for every-day use in our schools; in fact, the 
insufficiency of practical examples in arithmetic, has been 
a source of complaint for some time. The author having 
been connected with the Public Schools of this city 
since his earliest recollection, has had many facilities 
for collecting examples peculiarly adapted to the wants 
of the school, and he has long had them in manuscript, 
for his own particular use; on the recommendation of 
many teachers, they are now produced in the form of a 
book. 

The idea has been to collect all the varieties of 
examples that occur in the different arithmetics, and have 


465923 


vi PREFACE. 


them so arranged as will be most easy and useful to the 
mass of scholars attending the schools, and the arrange- 
ment of the subjects has been approved by all the pro- 
fession of the city, who have examined the manuscript, 
and in many cases has been suggested by them. 

The remainders in division are placed in the form ofa 
fraction, with the understanding that the number above 
the line is to be called the remainder, and the one below 
the divisor. 

After division, a few fractions used as multipliers and 
divisors, are introduced for the purpose of preparing 
the way for the $ and + used in denominate numbers, 
which immediately follow, and likewise, for affording as 
much as possible, that large class of children who leave 
school early, an opportunity to form some little 
acquaintance with fractions ; denominate numbers have 
been placed before fractions, because it is a subject, of 
which a knowledge is more easily acquired, and it is 
more pleasing to the pupil to step from division to 
denominate numbers, than to fractions. 

This arrangement has been objected to by some, on 
account of anticipating fractions; but if fractions be 
placed before denominate numbers there will be much 
more anticipated, or the subject will have to be inter. 
rupted by the interpolation of denominate numbers. 


Proportion does not occupy that prominent position 
that it does in some works; analysis, as can easily be 
seen from an examination of the book, is the ground- 
work for solving those questions formerly done by pro. 


PREFACE. viK 


portion. This subject is treated of, particularly in 
reference tu its qualities as a proportion. 

The answers are placed with nearly all the examples, 
on the ground, that they might as well be there as any- 
where else, for if a pupil is disposed to copy the answers 
in one case he will do it in another. 

A book without answers is a very unsatisfactory thing 
to teachers and pupils. 

The author takes this opportunity to express to his 
fellow teachers his most grateful acknowledgment for the 
universal kindness he has received from them, when 
their time and patience may have been taxed in review- 
ing the book, and furnishing many of the most prominent 
features ; and whether the experiment succeed or fail, the 
remembrance of their kind feelings towards him will ever 
be a source of pride and gratification. 


New Yorx, August, 1854. 
WM. H. REUCK, 


7 


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CONTENTS. 


PaGE. 

NGUGION BUG NUNICIBHOl ses es.st oa casree te esas Secitins as 1 
Simple Nmuibera ACCIUON: dees elec veacee atc» na/cjenay te 4 
“ ie MUDSAChON: wus eet sass 45's cee ens bale cure vi 

- “ MulGiplcationss.sace setts ame cnsee ceive v's LU 

fy . DYLVIRIOU 2 cia ad cslelei ste Mette aie sea ticle G1 e15 8ic iy 

Ms Promiscuous Examples. ..........e00- a ely 

bi te Supplement...... tise ete nue es AS SEKI me 4 
Federal Money. Reduction............0.4- Jestesoeeres aoe 
at . ASHEUION ste tis rae son's > re seemed eerie 32 

“ a SSUACACHOD eT see easy ae ees wna hehe eels 33 

$ - Multiplication....... eR OOae Saewe Of 

: - DIVISIOG iaees cee eete ee Wen sisteo sieves SLE 

- Promiscuous Examples. ........eee00- et 
Table of Weights, Measures, &c........... hese swe eres ce E40 
Denominate Numbers, Reduction..... Saledie cleeas lve seed 44 
“ « Reduction of Currencies.......... 55 

“ . AGCILION) So ceswadeecadasede's che euro t 

= . Suptractiony ss teda ade. aces eveneayel Oe 

. as Multiplication......... BOSC, lls 

“ s DivisiOUyareectitststee xs cs ere stat oe sane 69 

- < Promiscuous Examples........... 72 
Introduction to Fractions.......... Brees os Sarena ee 6 « te 
Vulgar Fractions. Reduetion.............. AREER: 
. : Additions; i vaeg ens s sss ies hs velcie eee 88 


- i Subtraction...... BAS WO s?e'n'n is Cae AES 91 


CONTENTS. 


Volgar Fractions. Multiplication. ©. c.J.00¢5 00: aves see « 


6 “ 
“ < 
« «“« 
é “ 
« iff 
a 6c 
« w 
“ « 


DIVISION 4 ois setae 
Promiscuous Examples. ........ee0s0s 


Reduction of Denominate Numbers.... 


Addition 
Subtraction 
Multiplication 
Division 


Prom. Exam. 


“ce 


“ 


ercoe 


Désimal Fractionas: <2. hc eke ee eae 


«“« 6 
e « 
« 66 
“ “ 
Ad «& 
“ «6 
«@ 
« 6 
“ « 
“ “ 
“« 66 
“« 119 
6c ot 


Percentage. eeeeeeoeeseereeneeeoeeeen#eenvpeeteee e@eeeoee0neese 
Commission..... 
Insurance eeseeeee eeeeeseeeeeseeeesoeeeeeeeeeeeeweeeeonee 


Rrokerage and Stocks. , 7 >. s~ccmieiies htaccess ¥es 


Perbereat tas cb i's eae a blecs So a oe c ete Tele sale okies stale suena 
ce Proplems Ade sisi.) ain eeaekinitin «Ca avo Bes sewer ee 
oS Partial Payments, « o esswo0c scnecnce ts esiemetcet 


Reduction of Decimal to Vulgar Fractions 


Addition®.% 2.2 te 


Subtraction ...... 


Multiplication......... 


Division, (20.6 Gans eeeoose eee 


Repeating Decimals....... 
Promiscuous Examples....... 


e@eeeeeevreeseeeee 


eeceeeeeeeeee ee 


eeeeeeeeeeve eee 


Reduction of Denominate Numbers.... 


Addition 
Subtraction 
Multiplication 
Division 
Prom, Exam. 


e@eeeevees 


@eeeeoeeeevneee ee eeerseeoeveee eee peeeee ee ee 


eeeoeve 


Compound WNtereat 120 o's 50's 0 5p oes ak Biss ec ae ae 


Misconnt.tosmee wees eee sak we se ne eitslstisie eis loc cial paicels 


Profit and TOMA Nias ccs 5000 0s cease pals <ha ets ae ae cats 


PAGE 

95 
100 
104 
106 
111 
113 
114 
115 
117 
119 
120 
121 
124 
125 
123 
181 
134 
139 
140 
141 
142 
144 
146 
148 
153 
155 
157 
160 
171 
173 
176 
178 
187 


CONTENTS. xi 


Pacr. 

WROOAU GOs ie estas oom iee a $10 ccs eis,e civiasiotamls siveste aces a NOLOE 
Proportion... wsccsesseseccccccssesssccesssenceosse 202 
OConipound Proportion saisetis sss ca ekid oss sins se vce sven es 209 
Practice <1. as's o< Dee e ecw ses casseseesVerewcvessesecveens Male 
Coston House! DUSMESS cc was oc sco'ssiesbiseee as scceee's cou MOLT 
RIATUBE A ater canes « ace ee nds oe Me lnae teens odes ce sence Thay 
AGERE CAIN piste aielsce trys siete v.a's So's owe eee tine ove eos see cee Doe 
Pm DGUnd MATMELEDI Ace's ss << ein Wiials Ped ses a0 6 oe en 50's snes 
Hq UntiGn Oe PAVINEMS sacle scinc'osisea aa 40s ota cdiveesaae ceweneoe 
Alig Atiotee Meas fen 6 occicis ssh oles cls Siee's ins 5 ¢ce Peer acme aoe 
e PANGELNRUG es iedaclgh tes aeeieerislepe as seats cemor 

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RUVOLGMION ares kins sicidie 2/00 ale titicanian hewens v4 ie eins + cee Moel 
PE CHSUPAEON rots s aisle 5 she initlo bis asia sida aisle» 4'e Nip Fo s'e 0 0,00 Sate 
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PRACTICAL EXAMPLES 


IN 


ARITHMETIC. 


NOTATION AND NUMERATION. 


ArticLe ]. What is ArirHMErtic ? 


Arithmetic is the science of numbers ; tt treats, 1st, of 
the elementary properties of numbers, 


2d. Of the operations upon numbers, called calculation. 
Arr. 2. What are the elementary rules of Arithmetic ? 


Notation and Numeration, Addition, Subtraction, 
Multiplication and Divison. 


Art. 3. What is Noration? * 


Notation is the art of writing numbers by figures or 
letters. 


Art. 4. What is NumMrEration 2 


Numeration ts the art of reading numbers when 
wretten, 


Art. 5, What are the two methods of Notation ? 

Arabic and Roman, 

Art. 6. What is the distinction ? 

The Arabic method 2s written by figures and the Roman, 
by letéers, 

Art. 7, What are the pe eniary, Jigures of all 
numbers 2 

1 


2 NOTATION AND NUMERATION, 


0 named nothing, zero or a cipher. 

2) 
seed one or a unit. 
2 “ two expressing two ones or two units. 
Do eee thres “ three... threes. 
dan four 3 four aT yt) + 
5 (49 five (74 five 66 [4 five (74 
6 (<4 six (19 SIX (44 (44 SiX <4 
T° © geven - seven **) “vseven - * 
8 “ — eight ° eight PS Pee ee 
27 Scene Hy nine Ef oe mi! ELITES Sete 


Notre.—The first of these is called the insignificant figure, from its nams, 
the others are called significant figures. Although Ois called the insignificant 
figure, it implies nothing only when written alone ; when it is placed to the 
right of any of the significant figures, it increases their value. 


Art. 8. What are the elementary letters that are used 
to express numbers ? 


I (one), V (five), X (ten), L (fifty), C (one hundred), 
D (five hundred), and M (one thousand). 


Art. 9, How are figures combined to form numbers 
greater than 9 ? 


By annexing the elementary figures to each other and 
giving a name to them according to the position which they 
occupy. Thus:— * 


3 
. 2 
n . a 
S | 8 eis 
Ae S AS a oot 
ee a Ho 363 
= & Boa ss 2 8 

rt 8 
Bg 8 8) ei Ong 
‘ar 63 3 a oS ee 
ae mm sige 2 oe 
ue Siete s aas Lie Se a 
See yO Tone Oe RD OS 5 Sie 
By §O bo OM MOM bet Dien aie Oy h Gms ° 
Sst NS Me, SS ay GS OS ate! are 
SSaem | 8) tas OS va te Sa So Sas 
RO ce ge, Olin aie SOU iets Os pat a eee ee 
on = = = 2) 
847298 659008765 


Art. 10. What is the rule for reading numbers ? 


Separate them into periods of three figures each, com- 
mencing at the right, and give to each period a name 
expressive of its value according to the following table ; 
the period to the right consists of units, tens,and hundreds, 
and each period to the left is sub-divided into units, tens, 


NOTATION AND NUMERATION. 3 


and hundreds of its own name. Then begin at the left and 
read towards the right, giving to each period its proper 
name and subdivisions. 


Undecillions. 
Decillions, 
Nonillions, 
Octillions 
eptillions 
extillions. 
Quintillions 
Quadrillions, 
Trillions 
Billions. 
Millions 
Thousands, 
Hundreds 


wm wn 
786, 530, 756, 783, 567, 806, 784, 527, 875, 611, 830, 956, 801, 


ae ee ee aan aA asa aan ae ena TC EO I ene ee 


Notre.—This mode of separating numbers, is called the French method, end 
is generally used in the United States. The English method is to sepzrate 
numbers into periods oi six figures. 

Art. 11, How are letters combined to express num- 
bers between those represented by single characters ? 

By repeating the same character, and by prefizing or 
annexing one of less value to one of greater. 

Note.—When a character of less value is prefixed to one of greater, it 


diminishes the greater by an amount equal to itself; when annexed, it 
tncreases the greater by an amount equal to itself. 


The following are some of the combinations :— 


I. (Two) XXI. (‘Twenty-one) 
ill. (Three) X XIX. (Twenty-nine) 
IV. (Four) XL. (Forty) 
VI. (Six) LX. (Sixty) 
VII. (Seven) XC. (Ninety) 
VII. (Hight) CX. (One hundred and ten) 
|X. (Nine) CXIX. (One hundred and nineteen) 
XJ. (Eleven) CCC. (Three hundred) 


XIV. (Fourteen) DCC. (Seven hundred) 
XVI. (Sixteen) MDCCC, (Eighteen hundred.) 
XIX. (nineteen) 

‘Art. 12. How many kinds of numbers are there ? 


Two ; simple or abstract and denominate numbers. 


Art. 13. What is a simple or abstract number ? 


It isa number not applied to things, as simply, 2, 8, 
1D) ec. 


4 SIMPLE NUMBERS, 


Art. 14. What is a denominate number ? 


It is a number applied to things, or having the 
name of some standard unit, as 2 apples, 6 pounds, 9 
bushels, &c. 


Note—The operations performed upon simple numbers are called tho 


simple rules; 
hen denominate numbers are composed of two or more denominations, 
they are somctimes called compound numbers. 


SIMPLE NUMBERS—ADDITION. 


Arr. 15, What is Apprrron ? 


Addition is the uniting of two or more numbers of the 
same name or kind into one. 


Art. 16. To add simple numbers, 


Rurz.—Place themone under another with units under 
wnits, tens under tens, hundreds under hundreds, &c., form- 
ing columns of units, tens, hundreds, dc. ; commence at the 
bottom of the column of units and add it upwards ; if the 
sum be 9 or less, set it down under the column of units ; 
if it be more than 9, set down the right hand figure under 
the column of units and carry the left hand figure or 
figures to the column of tens, and add it similarly to 
the column of units, place the right hand figure under the 
column of tens and carry the left hand figure or figures to 
the column of hundreds ; proceed in this manner to the last 
column when the whole amount must be set down. 


Art. 17, To prove Addition, 


Commence at the top of the column of units and add the 
several columns downwards. 


Notre.—The sign -+ (plus), denotes that the numbers between which it is 
placed are to be added. 

The sign = denotes that the number or quantities between which it is 
placed, are equalte cach other. Thus, 4-+2=6. 


ADDITION, 


(1.) (2.) (3.) (4.) 
234 3492 2841 2321 
177 1004 1876 462 
432 6570 2131 1874 
120 4211 1010 590 
963 15277 7858 5247 
(5.) (6.) (7.) (8.) 
1289 4691 9 459 
462 921 27 59 
1240 12 418 6759 
32 816 64 311 
475 1912 5419 109 
1894 8 315 
5392 8360 6252 7697 
(9.) (10.) (11.) 
98651 591863 37585 
6751 59007 5706 
989 8505 908 
5675 37805 718 
43506 8708 617 
86305 908 80956 
(12.) (18.) (14.) 

392860909 382569 2657800896 
11%75908 759089 95834926 
892358459 6678 7316919 
5736576789 98649 545837 
309208555 595009 168729449 
5007003835 


3J59555 


8095 


1* 


a ES 


S| 


6 SIMPLE NUMBERS. 


(15.) (16.) 


37580061 134138756291 
2109 51842655005620 
35708 2320047118577 
127059 1856007423856 
6551275 320148298008 
853875075 21208572968 


4278111 5197791199 


17. What is the sum of 307, 679, 4189, 7111, 816, 
995, 3307, 886, and 15? - Ans. 18305. 


18. What is the sum of 1801, 6911, 58, 79861, 4386, 
50015, 98653, 181615, 78216,-and 5006? 
Ans. 506522. 
19. What is the sum of 180560, 78100, 93775, 68722, 
500610, 8011561, 729816, and 440075? 
Ans. 5053219. 
20. What is the sum. of 351672, 335790, 698375, 
412793, 75211, 551692, 549006, and 17111 ? 
Ans. 2791650. 
21. What is the sum of two hundred and seven, three 
hundred and sixty-two, nine hundred and forty-five, two 
thousand three hundred and forty-three, fifteen thousand 
six hundred and twenty-two, and forty-five thousand and 
eight ? Ans, 64487. 
22. What is the sum of eighteen thousand three hun- 
dred and twenty, seventy-four thousand five hundred 
and six, two hundred and seventeen thousand nine hun. 
dred and twenty-one, fifty-three thousand seven hundred 
and eleven, five hundred and seventy-six thousand three 
hundred and four, and six hundred and fifty thousand 
and forty-four ? Ans. 1590806. 
23. Add 24 thousand 306, 150 thousand 525, 77 
millions 354 thousand 550, 680 millions 297 thousand 
002, 5 billions 72 millions 861 thousand 568. 340 tril- 


SUBTRACTION. — 


lions 750 billions 75 thousand and 2, 21 quadrillions 17 
trillions 702 millions 540 thousand 442 ? 
Ans. 21857756483303890. 
24, What is the sum of 864700 + 8687921 + 86470029 
-+ 3865007 + 6538219 + 1000 ? Ans. 95541876. 
25. What is the sum of 3886000591 +54631122 4- 
796351 + 84001 -+ $000 +86521-+ 3586004 8888888 + 
100000000 2 Ans. 550855074. 
26. What is the sum of 5863821-+78630-+ 8689 + 
3586722 + 8938042 + 75699 -+ 1400+ 8700963 + 44000 ? 
Ans. 18975476. 
27. What is the sum of 18+298+4621+89366-+ 
5096038 + 7863591 + 87963425 2 Ans. 96430917. 
28. What is the sum of 87006 292+ 98643821 + 
186911 4-'75201 + 6899+ 725+662. Ans. 97140415. 


SIMPLE NUMBERS.—SUBTRACTION. 


Art. 18. What is Suprractrion 2 


Subtraction is the finding of the difference between two 
numbers of the same name or kind. 


Art. 19. What are the terms used in Subtraction ? 

The Minuend or greater number, the Subtrahend or less 
number, and the Remainder, or difference between the 
greater ind less numbers. 


Art. 20. To subtract simple numbers, 


Rurun—Place the less under the greater, with units 
under units, tens under tens, dc. ; commence at the units 
and subtract each figure wn the subtrahend from the one 
above in the minuend, and set down the difference under 
the figures subtracted ; if any figure below, be greater than 
that above, add 10 to the upper figure and from the sum 


6 SIMPLE NUMBERS. 


subtract the one below ; set down the difference, add one to 
the next left hand figure of the subtrahend, and subtract 
as before. 


Art. 21. To prove Subtraction, 
Add the subtrahend and remainder together ; if the 
sum be equal to the minuend, the work ts right. 


Notr.—The — (minus), denotes that the numbers betweea which it ig 
placed are to be subtracted, the one having the sign before it, being the 
subtrahend. 


(1.) (2.) 
From 3725 Minuend. 75625 
Take 2164 Subtrahend. 24319 
Ans, 1561 Remainder, 51806 
1876781 36704527 
695845 10625365 
680936 26079162 
(5.) (6.) 
592700516 623115923 
81425307 451016100 
(7.) (8.) 
78629000 593567035 
17664508 96214073 
60964492 
(9.) (10.) 
1370426019 7910016302 
820512055 20081506 


7889934796 


(11.) (12.) 
872036005 123570000 
51052008 6720005 

(13.) (14.) 
316900082506 46299902756 
51120097805 589904756 

(15.) (16.) 
986150083555 713006542182 


96140076559 


63008400153 


17. From 758901 subtract 349806. Ans. 409095. 
18. From 829500 take 54650. Ans. 274850. 
19. From 720065991 take 12095899. 
Ans. 707970092. 
20. Subtract 390 from 10 600. Ans. 9610. 
21. Subtract 188605 from 189501. Ans, 896, 
22. What is the difference between 23800562 and 
199811 2 Ans. 2100751. 
23. What is the difference between 9859670800 and 
10906459860500 ? Ans. 10896600189700. 
24. If the sum of two numbers be 95000 and one of 
them be 8006, what will the other be ? 
Ans, 86994. 
25. If the sum of two numbers be 86957111, and one 
of them be 49963415, what will the other be ? 
Ans. 86993696. 
26. If the greater of two numbers be 3800011, and the 
less 290021, what is the difference ? Ans. 9990. 
27. There are two numbers, the greater is 40690080, 
and the less is 699090, what is the difference ? 
Ans. 39990990, 


10 SIMPLE NUMBERS. 


28. The difference between two numbers is 15986, 
and the greater is 1000000, what is the less number ? 
Ans. 986014. 

29. What is the difference between the sum of 

886951, 395867, and 880009, and the sum of 491611, 
8800, and 100000 2 Ans. 1062416. 

30. What is the difference between the sum of 

86900511, 8867592, 6750000, and 200000, and the sum 

of 35118672, 450000, 7000006, and 3008 ? 

Ans, 55146417. 

31. Ifa person have $4000 and lose $3010, how much 

will he have left ? Ans. $990. 


Notr.—$ is the sign for dollars. 
-32. If a merchant enter in business with a capital of 


$21308, and at the end of one year have $28105, how 
much will he have made 2? Ans. $6797. 


33. Suppose three persons commence business, the 
first putting in $35000, the second, $41700, and the 
third, $36150; if at the end of one year they have 
together $149711, how much will they have gained ? 

Ans, $36861. 


SIMPLE NUMBERS.—MULTIPLICATION. 


Art. 22, What is Muriprication ? 
Multiplication is the repetition of a number or quantity. 
Art. 23. What are the terms used in Multiplication ? 


They are the Multiplicand, the LA ge and the 
Product. 


Art. 24, What is the Multiplicand ? 


The Multiplicand is the number to be repeated or 
multiplied, 


MULTIPLICATION. 1} 


Art. 25. What is the Multiplier ? 


The Multiplier is the number of times that the multi- 
plicand is to be repeated. 


Art. 26, What is the Product ? 
The Product is the result of the repetition. 


Art. 27. What are the Multiplicand and Multiplier 
taken together called ? 


Factors. 


Arr. 28, What is a Composite number ? 


A Composite number is one that is composed of two 
or more factors. 


Arr. 29, To multiply simple numbers, 


Ruitz.—Place the multiplier under the multiplicand, 
units under units, tens under tens, ke. 

I. Lf the multiplier be 12 or less, multiply the units of 
the multiplicand by the multiplier ; set down the units of 
the product under the units of the multiplier, and carry 
the remaining figure or figures to the product of the tens 
of the mulliplicand by the multiplier ; place the right 
hand figure of this result under the tens of the multiplier 
or multiplicand, and carry the remaining figures to the 
product of the hundreds of the multiplicand by the multe 
plier ; proceed in like manner to the last figure of the 
multiplicand, when the entire result must be set down. 

I. Lf the multiplier be greater than 12, multiply the 
multiplicand by each figure of the multiplier separately, 
commencing with units, and set the products under each . 
other, observing to place the right hand figure of each 
product under that figure which is used as a multiplier ; 
add the several products together, and their sum will be the 
entire product. 


Art. 30. To prove Multiplication, 


Roie.—Make the Multiplier the Multiplicand, or add 
the figures that compose the multiplicand, and when the 


12 SIMPLE NUMBERS. 

sum is 9 or more, reiect 9 and add the remainder to the 
succeeding figures, and place the last remainder opposite the 
Multiplicand ; proceed thus with the Multiplier and Pro- 
duct; then multiply the remainders of the Multiplicand 
and Multiplier, and reject the 9’s ; if the remainder be the 
same as that of the product, the work is very likely to be 
correct. 


Note —The sign x denotes that the numbers between which it is placed 
are to be multiplied together. 


ABBREVIATED TABLE FROM 1 To 9. 


2x2= 41)3x6=18!6x6=386 
2x38= 6|4x5=20/5x8=—40 
2x4— 813X731) Ox v2 
38X3— 91/38x8=24|5x9=—45 
2%5=10/4x*6=2416x8=—48 
2x6=1215x5=25|7x7=—49 
3X4=1213x9=27|6x9=54 
De A Xie | oC OG 
3xX5—15|5x6—30|8x8—64 
2x8=16|4x8=32/8x9=72 
4x4=16|5x7=35!19x9=—81 
2x9=—18 |4x9=36 
COMPLETE TABLE FROM | To 12. 
Ve Sr Sora Os ea 
Ot OAN SS UIO Pie 14716)" 18) 201 27 4 
BiG) 9112 eel eee ie oO 3/1 3 
4} 8|12/16/20/24)|28)|32| 36] 40] 44) 48 
| 5110!15; 20) 25] 30) 385/40) 45] 50! 55! 60 
6| 12] 18 | 24/30] 386)42|48] 54] 60] 66) '72 
7114] 21) 28|35|42149)56! 63| 70| 77; 84 
8| 16 | 24] 32|40| 48/56/64] 72}| 80] 88! 96 
9|18 | 27 | 86 | 45| 54) 63/724 81] 90] 99! 108 
10/20/30] 40/50 60/70} 80} 901100] 110) 120 
1-11) 22) 33 | 44] 55| 66|'77| 88} 99) 110) 121) 182 
12 | 241 86 | 48] 60/ 72) 84) 96/ 108/ 1201182 144 


{ 


CO D =F Sd Ct H& CD dS we 


MULTIPLICATION. 


. Multiply 64738 by 17. 
. Multiply 48786 by 19. 


- Multiply 355 by 2. Ans. 710, 
- Multiply 811 by 3. Ans. 2483, 
. Multiply 923 by 5. Ans. 4615, 
. Multiply 1816 by 4. Ans. 7264, 
. Multiply 3061 by 7. Ans. 21427, 
. Multiply 763 by 8. Ans. 6104, 
. Multiply 1412 by 6 Ans. 8472, 

Multiply 769 by 6. Ans. 4614, 
, Multiply 3501 by 5. Ans. 17505. 
. Multiply 7108 by 7. Ans. 49756, 
. Multiply 8009 by 8. Ans. 24072, 
. Multiply 7110 by 9. Ans. 63990, 
. Multiply 1429 by 4. Ans. 5716, 
. Multiply 1717 by 5. Ans. 8585, 
. Multiply 1919 by 6. Ans. 11514, 
. Multiply 7285 by 8. Ans. 58280, 
. Multiply 842 by 9 Ans. 7578, 
. Multiply 687 by 7. Ans. 4809, 
. Multiply 1845 by 12. Ans. 16140, 
. Multiply 6843 by 18. Ans. 88959, 
. Multiply 7567 by 15. Ans. 113505, 
. Multiply 4766 by 14. Ans. 66724, 
. Multiply 5879 by 18. Ans. 105822, 
. Multiply 17886 by 16. Ans. 278176. 


Ans. 1100546. 


Ans. 831934. 


. Multiply 7942375 by 17. 
. Multiply 8867592 by 19. 
. Multiply 659832 by 16. 
. Multiply 463758 by 13, 
. Multiply 886758 by 21. 
. Multiply 486239 by 49. 
. Multiply 386724 by 87. 
9 


. What is the product of 756839 x 14 ? 


Ans, 10595746. 


. What is the product of 367587 x 15 ? 


Ans. 5513805. 


. What is the product of 487986 x 18 ? 


Ans. 8783748. 
Ans. 135020375. 
Ans. 73484248, 
Ans. 10557312. 
Ans. 6028854. 
Ans. 8121918. 
Ans. 23825711. 
Ans. 338644988, 


14 SIMPLE NUMBERS. 


37. Multiply 44670 by 145, Ans. 6477150. 
388. What is the product of 763521 x 488 ? 
Ans. 834422198. 
39, What is the product of 367950 x 756% 
Ans. 278170200. 
40, Multiply 78609 by 406. Ans, 31915254, 
41. Multiply 887002 by 903. Ans. 800962806. 
42. Multiply 7532100 by 4861. 
Ans. 36613588100. 
43, Multiply 684207 by 7006. 
Ans. 4793554242, 
44, Multiply 75862 by 8076. = Ans. 612661512. 
45, Multiply 867925 by 40608. 
Ans. 85244698400. 
46. Multiply 76528 by 84793 Ans. 64890388704. 


Art. 31, To multiply by 10, 100, 1000, &c., 


RuLe.— Annex as many ciphers to the multiplicand as 
there are ciphers to the right of the seyhieyicanel Fier of the 
multiplier. 


47, Multiply 715 by 10. Ans. 7150. 
48, Multiply 4685 by 100. Ans. 468500. 
49, Multiply 781954 by 1000. Ans. 781954000. 
50. Multiply 2875 by 16000. Ans. 28750000. 
51. Multiply 486 by 100. Ans. 43600. 
52. Multiply 86735 by 1000. Ans. 86735000. 


53. Multiply 16392 by 10000. Ans. 163920000. 


Art. 32. To multiply when there are ciphers to the 
right of the multiplier or multiplicand, or both, 


Ruite.—Leglect the ciphers on the right of the multi- 
plicand and multiplier, and multiply the remaining num- 
bers together ; to the product annex as many ciphers as 
were neglected zn the factors. 


54. Multiply 6852 by 120. Ans. 822240. 
55. Multiply 7568 by 150. Ans. 1135200. 
56. Multiply 46780 by 1380. Ans 6081400 


MULTIPLICATION. 


. Multiply 17565 by 1800. Ans. 31617000. 
. Multiply 48450 by 1700. Ans. 73865000. 
. Multiply 685900 by 190. Ans, 130321000. 
. Multiply 76980 by 16000. Ans. 1231680000. 
. Multiply 78660 by 1400. Ans. 110040000. 
. Multiply 708060 by 490. Ans. 846949400. 
. Multiply 38506 by 43800. Ans. 1686562860. 
. Multiply 69870 by 70800. Ans. 4946796000, 
65. 


What is the product of 72893 by 409800. 
Ans. 29871551400. 


. What is the product of 5620800 by 228800 2 


Ans. 1286039040000. 


. Multiply 986000 by 4950000. 


Ans. 4880700000000. 


. Multiply 40996200 by 708060. 


Ans. 29027769372000. 


. Multiply 5900863700 by 8006100. 
47242904868570000, 
. Multiply 986105092 by 750036. 


Ans. 7896143187833 12. 


. Multiply 49271156000 by 1880600. 


Ans. 92659335973600000. 


. Multiply 783385505 by 730001. 


Ans. 571835701985505. 


. Multiply 92376472 by 8000706. 


Ans. 739076993789282. 


Arr. 33. To abbreviate multiplication when the 
multiplier is from 1 to 12 above or below 100, 1000, 
10,000, &c., 


Rutz.— Multiply by 100, 1000, or 10000, &c., and te 


this product add as many times ihe multiplicand as the 
multiplier exceeds 100, 1000, &c., or subtract as many 
times the mulliplicand as the multeplier is less than 100, 


1000, de. 
74, Multiply 718 by 101. Ans, 72518, 
75. Multiply 399 by 102. Ans. 40698. 
76. Multiply 4118 by 103. Ans, 424154. 


16 


SIMPLE NUMBERS. 


. Multiply 5612 by 106. 


Ans. 594872, 


78. Multiply 4610 by 111. Ans. 511710, 
79. Multiply 5816 by 109. Ans. 633944, 
80. Multiply 8916 by 108. Ans. 962928, 
81. Multiply 9871 by 105. Ans. 1056455, 
82. Multiply 5714 by 107. Ans. 611898, 


83. Multiply 7101 by 110. Ans. 781110. 
84. Multiply 5806 by 1006. Ans. 5840836. 
85. Multiply 754 by 1011. Ans. 762294, 
86. Multiply 869 by 10009. Ans. 8697821, 
87. Multiply 386 by 99. Ans. 38214, 


88. Multiply 7815 by 98. Ans. 765870, 
89. Multiply 6188 by 97. Ans. 600236. 
90. Multiply 7289 by 999. Ans. 7281711. 


. Multiply 88751 by 998. 
. Multiply 67583 by 996. 
. Multiply 74189 by 995. 


Ans. 38673498, 
Ans. 67312668. 
Ans. 78818055. 
Ans, 48283907, 


94, Multiply 48677 by 991. 
95. Multiply 786511 by 992. Ans. 780218912. 


Art. 34. The value of a single article being known, 
now can the value of any number of articles of the same 


kind be found 2? 


Ruitz.—Multiply the value of a single article by the 
number of articles. 
Norr.—The student will remember that the result will be thesame which 


ever factor he makes the multiplier. He should, for expedition, choose the 
smaller for the multiplier. 


96. If one pound of sugar cost 8 cents, what will 450 
pounds cost ? Ans. 3600 cents. 

97. If one pound of beef cost 13 cents, what will 692 
pounds cost ? Ans. 8996 cents. 

98. If one yard of cloth cost 19 shillings, what will 
289 yards cost ? Ans. 5491 shillings, 

99. If one barrel of pork cost $15, what will 1728 
barrels cost ? Ans. $25920, 

100. If a car can go 35 miles in one hour, how far can 
it go in 425 hours ? Ans, 14875 miles. 


DIVISION. 17 


101. If sound travels 1420 feet in one second, how far 
will it travel in 190 seconds 2 Ans. 269800 feet. 
102. If you can purchase 250 apples for one dollar, 
how many can be bought for $763 ? 
Ans. 190750 apples. 
103. If it require 720 barrels of provisions to sapply 
an army for one day, how many barrels will be required 


for 865 days? Ans. 262800 barrels. 
104. If one acre of land cost $9620, how much will 
736 acres cost ? Ans. $7080320. 


105. If it cost $98650 to build one mile of railroad, 
how much will it cost to build 2809 miles ? 
Ans. $277107850. 


SIMPLE NUMBERS.—DIVISION. 


Art. 35. What is Division 2 


, Division is the method of finding how many times one 
number ts contained in another. 


Notr.—Division may likewise be defined as the separation of a number into 
equal parts. 


Art. 36. What are the terms used in Division 2 

They are the Divisor, Dividend, Quotient, and 
Remainder. 

Art. 37. What is the Divisor ? 


The Divisor is the number that 7s contained in another. 
Art. 38. What is the Dividend 2 
The Dividend is the number that contains the divisor. 


Art. 39. What is the Quotient ? 


The Quotient is the number of times the divisor is con 
tained in the dividend. 
Ox 


18 SIMPLE NUMBERS. 


Art. 40. What is the Remainder ? 


The Remainder is what is left when the division is no 
exact, and is usually written above the divisor with a 
horizontal line between, and in this form is annexed to 
the number in the quotient’s place to form the complete 
quotient, 


Art. 41, To divide Simple Numbers, 


Rutz.—Placé the divisor to the left of the dividend ; 
jind how many trmes it is contained in the first figure or 
Sigures of the dividend, and place the number of times thus 
found below or to the right of the dividend for the jirst 
figure of the quotient ; multiply the divisor by this figure, 
and subtract their product from the figure or fiyures of the 
dividend which were divided; to the remainder annex the 
next figure of the dividend and divide the number thus 
formed by the divisor for the second figure of the quotient. 
Multiply the divisor by this figure and subtract the pro- 
duct from the last number divided, annex the next figure 
of the dividend to the remainder, and so proceed until all 
the figures of the dividend are successively used. 

Noter.—If the divisor be 12 or less, the quotient is placed below the dividend, 


and the process is called short division ; if more than 12, the quotient is placed 
to the right, and the process is called long division. 


Art. 42. To prove Division, 


Rutz.—Multiply the divisor by the quotient and add 


in the remainder ; if the result be equal to the dividend the 
sum ws right. 


Notz.—The sign —— denotes that the numbers between which it is pleced 
are to be divided, the divisor being to the right; frequently a horizontai line, 
having the dividend above and the divisor below, is used as a sign of 
division. 


1. Divide 16296 by 6. Ans, 2716. 
2. Divide 18279 by 9. Ans. 2031. 
3. Divide 997885 by 7. Ans. 142555. 
4. I)ivide 17629720 by 8. Ans. 22038715. 
5. Divide 3729602975 by 5. Ans, 745920595, 
6. Divide 1793990154 by 11. Ans. 163090014. 


19 


DIVISTON. 
7. Divide 144073456956 by 12. 
Ans, 12006121413. 
8. Divide 367981 by 18. Ans, 28306;%5. 
9. Divide 6789341 by 14. Ans, 484952132, 
10. Divide 984673 by 14. Ans. 7088314, 
Ll. Divide 1146792 by 15. Ans. 7645212, 
12. Divide 915673 by 13. Ans. 70436 5. 
13. Divide 4699285 by 17, Ans. 276428 
14. Divide 683295 by 19. Ans, 8596214, 
15, Divide 5126788 by 18. Ans, 284813814. 
16. Divide 8643791 by 16. Ans. 54023615. 
17. Divide 1985637 by 16. Ans. 124102,°,. 
18, Divide 3867598 by 19. Ans. 177242. 
19. Divide 6785721 by 20. Ans. 339286.),. 
20. Divide 75632871 by 20. Ans. 878164321, 
21. Divide 186593 by 21. Ans. 8885,8,. 
22. Divide 7862093 by 27. Ans, 29118814, 
23. Divide 8536752 by 36. Ans. 237132. 
24, Divide 78632900 by 55. Ans. 1429689. 
25. Divide 88265381 by 96. Ans. Bee 7 
26. How many times is 154 contained in 78422001 ? 


. How many times is 297 contained in 8075208 U 


. How many times does 55770088 contain 4 


Ans. 509235112 


4° 


Ans. 18021925! 


z 
a? 
2 
8: 


rs Boek 


"ore wed 


Ans. 1149894 


. How many times does 3862951 contain 225 ? 


Ans. 17168381. 


b 


30. What is the quotient when 7589901 is divided by 
753 2 Ans, 10079444, 
31. Divide 675113821 by 699. Ans, 96582283. 
82. Divide 8526955 by 488. Ans. 17063211, 
33. Divide 722386 by 731. Ans, 997229. 
34, Divide 2226985 by 1802. Ans. 12351272. 
35. Divide 88659110 by 2012. Ans. 19214642, 
36. Divide '78611003 by 2309, Ans. 340451293. 
37. Divide 4845167 by 3605. Ans. 1384343832, 
88. Divide 9863701 by 808. Ans. 12207448. 
89. Divide 4816657 by 9101. Ans. 5292423, 


20 SIMPLE NUMBERS. 


40. Divide 7712866 by 5888. Ans. 13098478, 
41. Divide 5379115 by 2986. Ans, 18014322, 
42. Divide 88870054 by 8677. — Ans. 44225 a tr 
43, Divide 75867308 by 10115. Ans. 7500;48%°.. 
44, Divide 67984000 by 30412. Ans, 223513189, 
45. Divide 68333867 by 49766. Ans. 1373757 66 
46. Divide 48659910 by 54001. Ans. 9013%°S 


Arr. 43. To divide when the divisor has ciphers 
annexed, 


Ruitz.—Reect the ciphers on the right of the divisor, 
and point off as many figures on the right of the dividend 
as there are ciphers rejected on the right of the divisor ; 
proceed with the remaining numbers of the divisor and 
dividend, according to the rule for division, and to the 
remainder, if there be one, annex the figures pointed off 
From the dividend, to obtain the complete remainder ; if 
there he no remainder after dividing, the numbers pointed 
off in the dividend will be the remainder. 


47. Divide 8820 by 60. Ans. 147. 
48. Divide 3637800 by 90. Ans. 40420. 
49. Divide 5639651500 by 700. Ans. 8056645. 
50. Divide 79864931 by 110. = Aus. 7126044775. 
51. Divide 7386008 by 1200. Ans. 6155 7995- 
52. Divide 683759 by 130. Ans. 5259-6 
3. Divide 7964110 by 1500. Ans. 5309-610 
54. Divide 56793411 by 14000. Ans. 40564255. 
55. Divide 3387861 by 170. Ans. 1992 
56. Divide 4867584 by 1700. Ans. 25697 
57. Divide 78600592 by 1900. Ans. 41368 
58. Divide 58677000 by 1800. Ans. 32598,° 
59. Divide 78659287 by 3860. Ans. 20878¥ 
60. Divide 99115601 by 7700. Ans. 128722: 
61. Divide 75116729 by 134000. 
Ans. 56073700: 
62. Divide 59867200 by 786000. Ans. 76121209, 
63. Divide 511729850 by 590000. 
Ans. 867330500: 


al 
oc} etiosl 


Neal’ A) os enige Cl De 


DIVISION. Ot 


Art. 44, What is a prime number ? 


A prime number is one that cannot be divided without a 
remainder, by any number except itself and unity, as 1, 2 
30. be Lily L Ourcce 


Art. 45, What is a Composite number ? 


A composite number is one that can be divided by other 
numbers than itself or unity without a remainder, as 6 
9, 16, dc. ; or a composite number is one that is composed 
of two or more factors. 


Arr. 46, When are the factors said to be prime ? 
When they are all prime numbers. 


Art. 47. To separate a number into two factors, 


Ruitz.—Divide the given number by any number that 
will divide it without a remainder; the divisor will then be 
one factor, and the quotient the other. 


Arr. 48. To separate a number into three factors, 


Rutz.—Tirst separate it into two factors, and then, one 
of those factors into two others. 


Art. 49. To separate a composite number into its 
prime factors, 


Ruie.—Separate the given number into two factors, and 
these factors into others, until the last factors are prime 
numbers ; a collection of all these factors, will be the prime 
factors of the given number, 


64, What are two factors of 72? 
Ans. 12 and 6, or 8 and 9, &c. 


Notr.—This and some of the succeeding examples may be divided into a 
variety of factors. 


65. What are two factors of 182? 
Ans. 12 and 11, or 3 and 44, &c. 

66. What are two factors of 441 2 
Ans, 21 and 21, or 7 and 68, 


22 SIMPLE NUMBERS. 


67. What are three factors of 360 ? 
Ans. 12, 3, and 10, or 6, 5, and 12, &c. 
68. What are three factors of 462 ? " 
Ans. 6, 7, and 11. 
69. What are three factors of 1560 ?. 
Ans. 10, 12, and 18. 
70. What are the prime factors of 18 ? 
Ans, 2, 3, 3. 
71. What are the prime factors of 86 ? 
Ans, 2, 2, 3, 3. 
72, What are the prime factors of 128 ? 
Ans, 2, 2, 2, 2,2, 2, and 2. 


Art. 50. To divide by a composite number, 


RuLE.— Divide the given dividend by one factor of the 
divisor, and then divide the quotient thus obtained by 
another factor, and so proceed until all the factors have 
been used as divisors. 


Arr. 5]. To find the complete remainder, 


Rute.—Multiply the second remainder by the first 
divisor, and add in the first remainder ; the result will be 
the complete remainder for the first two divisions ; of there 
be a third divisor, multiply the remainder by the product 
of the two previous divisors and add in the complete 
remainder arising from the first two divisions ; the result 
will be the complete remainder for three divisions ; if there 
be a fourth, or succeeding divisors, proceed in a like 
manner. 


73. Divide 17496 by 36, separated into two factors, 
Ans. 486. 

74. Divide 98710 by 84, separated into two factors, 
_ Ans, 117539. 

75. Divide 66921 by 88, separated into two factors, 
Ans. 7604}. 

76. Divide 54833 by 108, separated into two factors 
Aus. 507 75'5 


DIVISION. 23 


77. Divide 127563 by 156, separated into two factors. 
Ans. 817}44. 

78. Divide 946729 by 180, separated into two factors 
Ans. 52593928, 

79 Divide 598486 by 169, separated into two factors, 
Ans. 3541745. 

80 Divide 190000 by 225, separated into two factors, 
Ans. 844399. 

81. Divide 16781200 by 1728, separated into three 


factors. Ans, 971177735: 
82. Divide 7286511 by 729, separated into three 
factors. Ans. 999515. 
83. Divide 158672951 by 1296, separated into three 
factors. Ans, 122482739 3. 
84. Divide 5987726 by 576, separated into four 
factors. Ans. 10395228, 


Art. 52. To abbreviate division when the divisor and 
dividend have one or more common factors, 


Ruie.— Omit the common factor or factors, and then 
divide the product of the remaining factors of the dividend 
by that of the divisor. 


N oTe —This omission of common factors is called Cancellation. 


86. Divide 6x7 x9 by 3x7 Ans. 18, 
87. Divide 4x8 x15 by 2x35. Ans. 16, 
88. Divide 8x9x 12x16 by 8x9x24. Ans. 8 
89. Divide 3X5 x16 x27 by 8x10 12, 

Ans., 18. 
90. Divide 7xX9«15 x50 by 5X7X6. Ans. 225, 
91. Divide 2x 18 X55 x 100 by 8x 11x 20. 


Ans. 300. 
92. Divide 40 x50 x 500 by 4x10 100. 

Ans. 250. 
93. Divide 1296 by 48. Ans. 27. 
94. Divide 16380 by 1260. . Ans. 13. 
95. Divide 367400 by 2200. Ans. 167. 


96. Divide 26x73 x 115 by 5x26. = Ans. 1679. 


24 SIMPLE NUMBERS. 


97. Divide 708 x 1000 x 4500 by 36 X50 x 75. 
Ans. 23600 
98. What is the quotient of 108—9? Ans. 12. 
99, What is the quotient of 2016-36? Ans. 56, 
100. What is the quotient of 419454 ? 
Ans, 7738, 
101, What is the quotient of '718677—87 ? 
Ans. 826084, 
102. What is the quotient of 1890018408 ? 
Ans. 463218 
103. What is the quotient of 7x 12~6 x7? 
Ans. 2. 
104. What is the quotient of 5x6 x 100+4 x6 x25! 
Ans. 5. 
105. What is the quotient of 200 x 225 x 460—20 x 
23 X25? Ans. 1800. 
106. What is the quotient of 69 x 450 x '7000—3 x 
14x15 x50? Ans. 6900. 


107. What is the quotient of +28? 2 Ans, 32. 
108. What is the quotient of 14750 2 Ans. 59. 


109. What is the quotient of —; 3 “; S oo 22 Ans, 42983, 
110. What is the quotient of - 2009 ? Ans, 28738 


111. What is the quotient of 73°27 2 Ans, 14, 
112. What is the quotient of #2~2#&*550 9 


5x12x55 

Ans, 240 
113. What is the quotient of 72~**? Ans, 6 

114. What is the quotient of —395- 1 z 4 8 8 ? 
Ans. 601382 
- 115. What is the result of 38 x 152 Ans, 30. 
116. What is the result of %° x10? Ans. 180. 
117. What is the result of 75 x12? Ans. 60. 


118. What is the result of 259x252 Ans, 125. 
119. What is the result of &,° x 34 2 Ans, 90. 


DIVISION. 25 


120. What is the result of x i 2 
Ans. 6380. 


8649 


121. What is the result of ->3- X36? 
Ans. 17298. 


Art 53, When the number of articles and their value 
are known. how can the value of a single article be 
found ? 


Rutz —Divide the value of all the articles by the num- 
ber of articles ; the quotient will be the value of a single 
article, 


Art. 54. When the value of a single article and the 
value of several articles are known, how can the number 
of articles be found ? 


Rute.— Divide the value of all the articles by the value 
of a single article ; the quotient will be the number of 
articles, 


Notre.—The divisor and dividend should always be of the same name, except 
when the value of a single article is to be found. 


122. If 25 bushels of wheat cost $50, what will one 


bushel cost ? Ans. $2, 
123. If 64 barrels of wheat cost $448, what will one 
barrel cost ? Ans. $7. 
124. If 75 hogsheads of sugar cost $1200, what will 
one hogshead cost ? Ans. $16. 
125. If 725 acres of land cost $49300, what will one 
acre cost ? Ans. $68. 
126. If 950 suits of clothes cost $35150, what will one 
suit cost ? Ans. 37. 
127. If one barrel of pork cost $13, how many barrels 
can be bought of $12285 ? Ans. 945 barrels. 


128. If $3550 will buy one house, how many houses 
of the same value each, will $102950 buy ? 
Ans. 29 houses, 
3 


26 SIMPLE NUMPERS, 


129. If a person can walk 29 miles a-day, how many 
days will it take him to travel 22098 miles ? 
i) Ans. 762 days. 
130. If a person can count 6800 in an hour, how many 
hours will it take him to count 31769600 ? 
Ans. 4672 hours. 
131. If it cost $30000000 to construct a railroad 384 
niles long, what will be the average cost a mile ? 
Ans, $78125. 


PROMISCUOUS EXAMPLES. 


Nore.—In the following sums, it is a very useful and interesting exercise ta 
indicate the operations to be performed. 


1. If 9 pounds of sugar cost 63 cts., what will 1 pound 
cost? What will 14 pounds cost? Ans. 98 cents. 
2. If 12 yards of cloth cost $72, what will one yard 


cost? What will 56 yards cost ? Ans. $356. 

3. If 13 yards of velvet cost $65, what will 19 yards 
cost ? Ans, $99. 

4, If 29 bushels cost 754 pence, what will 35 bushels 
cost ? Ans. 910 pence. 

5. If 2138 yards of cloth cost $852, what will 254 
yards cost ? Ans. $1016. 

6. If 211 pounds of tea cost 17724 cents, what will 
628 pounds cost ? Ans. 52752 cents. 


7. If you can buy 765 yards of muslin for $51, how 
many yards can you get for $3876? Ans. 5640 yards. 
8. If you buy 3420 oranges for $76, how many can 
you buy for $37? Ans. 1665 oranges. 
9. If you can buy 87724 bricks for $964, how many 
can you buy for $4292 Ans. 39039 bricks. 
10. If 75 yards of cloth cost $375, how many yards 
can be bought for $1865 2 Ans. 373 yards, 
11. If 38 acres of land cost $11172, how many acres 
can be bought for $107310 ? Ans, 365 acres. . 


PROMISCUOUS EXAMPLES. 97 


¢ 
12. If 487 acres cost $2713877, how many acres can be 


bought for $581256 ? Ans. 936 acres. 
13. What will 1659 sheep cost at the rate of 624 
shillings for 13 sheep ? Ans, 79632 shillings. 


14. If 1000 feet of lumber cost 6000 cents, how many 
feet can be bought for 161400 cents ? 
Ans, 26900 “eet. 
15. If 100 pounds of pork cost 1400 cents, what will 
L786 pounds cost ? Ans, 25004 cents. 
16, A person had five houses: he sold one for $3820, 
another for $6364, the third for $4840, the fourth for 
$5600, and the fifth for $7260; he divided the amount 
equally between his 4 children, how much did each 
one receive ? Ans. $6971. 
17. A person in business gained $4250 a year for 5 
years: he then lost $984 a year for 4 years, and the 
rollowing year ho gained $4866, how much was his 
average gain a year ? Ans. $2218 gain. 
18. If a person buys 7881 pounds of sugar at 8 cents 
a pound, how many pounds of coffee at 11 cents a pound 
can he receive in exchange for the sugar ? 
Ans. 5368 pounds. 
19. If 600 barrels of flour at 7 dollars a barrel, cost 
$4200, how much will 8861 barrels cost ? 
Ans. $27027. 
20. A merchant had a capital of $30000; during the 
first year that he was in business, he gained $4000, in 
the second $5000, the third year he lost $1400, when he 
retired from business, and purchased property, by the 
sale of which he doubled his money ; he then kept $50000 
for himself, and divided the rest equally between his 3 
sons ; how much did each receive ? Ans. $8400. 
21. A person bought 38 hogsheads of sugar, each 
weighing 1240 pounds, for which he paid 9 cents a 
pound, how much did the whole cost ? 
Ans. 83480 cents. 
22. A person sold 4 pieces of cloth, which ineasured 
as follows: the first two pieces contained 45 yards each. 
the third picce contained 47 yards, and the fourth, 


28 SIMPLE NUMBERS, 


o3 yards; the whole cost $760; how much would that be 
for 50 yards? Ans. $200. 
23. If 350 acres of land worth $275 an acre, and 490 
acres worth $300 an acre, be exchanged for 70 houses, 
what will be the price of each house, supposing them to 
be of equal value ? Ans. $3475. 


SUPPLEMENT 


Art. 55. If any number be divided by 2, 


Lt will be separated into two equal parts, each of which 
is called 4 (one half) of the number, and the two parts 
% (two halves,) or the number ttself. 


Art. 56. If any number be divided by 3, 


Lt will be separated into three equal parts, one of which 
ts called 4 (one-third) of the number, two, 2 (two-thirds) 
and three, % (three-thirds) or the number itself. 


Arr. 57. If any number be divided by 4, 


Lt will be separated into four equal parts, one of which 
is called 1 (one-quarter) of the number, two, 2 or 4 (two- 
quarters or one-half) three, 2 (three-quarters) and four, 
4 ( four-fourths) or the number itself. 

Notr.—These forms, 4, 4, 3, &c., are called fractions,or broken numbers, 


and may be extended to fifths. sixths, &c. The number above the line is 
called the numerator, and the one below, the denominator. 


Arr. 58. To multiply a number by a fraction. 


Rurze.— Divide the given number by the denominator, 
and nvultiply the quotient by the numerator. 


Arr. 59. To multiply one number by another having 
a fraction attached to it. 


Ruie.—WMultiply by the fraction first, and to the result 
add the product of the two whole numbers. 


SUPPLEMENT, 29 


1. Multiply 186 by 4. Ans. 93, 
2. Multiply 186 by 2. Ans. 62, 
5. Multiply 986 by 2. Ans. 498, 
4. Multiply 1464 by 1. Ans. 366, 
5. Multiply 1311 by 2. Ans. 874. 
6. Multiply 1687 by 1 Ans. 8431, 
7. Multiply 12956 by 3. Ans. 9717, 
8. Multiply 682 by 31. Ans. 23887, 
9. Multiply 1496 by 5}. Ans. 8228. 
10. Multiply 8856 by 6k Ans. 24100, 
11. Multiply 9259 by 301, Ans, 2800843, 
12. Multiply 14591 by 691, Ans. 10140741, 
13. Multiply 1825 by 3651, Ans. 6665811, 
14, Multiply 18879 by 2872. Ans. 5430859. 
15. Multiply 7864 by 683. Ans. 540650. 
16. Multiply 5897 by 813. Ans. 4820792. 
17. What cost 76 bushels of oats at 374 cents a 
bushel ? Ans. 2850 cents. 


18. What cost 984 yards of cloth at $3} a yard ? 
Ans. $3198. 


19. What is the value of 729 acres of land at $552 an 


acre ? Ans. $388 194, 
20. If one pound of butter cost 314 cents, what will 
988 pounds cost ? . Ans, 30875 cents. 


21. If one pound of tea cost 621 cents, what will 4 


boxes that contain 62} pounds each, cost ? 
Ans. 15625 cents. 


22. If 2721 square feet make one square pole, how 


many square feet will make 38 square poles ? 
Ans. 1088554 square feet. 


23. If 3652 days make one year, how many days froin 


the year 1788 to 1854 ? Ans, 241061 days. 
24. What will 1497 yards of silk cost at 682 cents'a 
yard ? Ans. 1029183 cents, 


Arr. 60. To divide a number by a fraction, 


Ruise.— Multiply the given number by the denominator 
and divide the product by the numerator. 
3% 


30 SIMPLE NUMBERS. 


Art. 61. To divide one number by another number 
having a fraction annexed to it, 


Ruitz.—Arrange the numbers for division ; multiply 
both the divisor and the dividend by the denominator of the 
fraction, observing in the divisor to add in the numerator , 
divide the numbers thus formed, and the quotient will be 
the answer ; if there be a remainder it will be halves if ihe 
divisor was multiplied by 2, thirds if the divisor was 
multiplied by 3, fourths or quarters, if by 4, &c. 


25. Divide 325 by 22. Ans. 1380. 
26. Divide 627 by 5}. Ans, 114. 
27. Divide 750 by 61. . Ans. 120 
28. Divide 1811 by 123. Ans. 104 rem. 11. 
29. Divide 725 by 33. Ans.-217 rem. 12. 
30. Divide 6211 by 83. Ans. 745 rem. 22. 
31. Divide 1900 by 162. . Ans. 114, 
32. Divide 3556 by 303. Ans. 115 rem. 193. 
33. Divide 7926 by 2721. Ans. 29 rem. 803. 
34. Divide 18464 by 69}. Ans. 265 rem. 463. 
35. Divide 7598 by 873. Ans, 86 rem. 513. 


36. Divide 34788 by 83}. Ans. 1043 rem. 21. 
37. If 5£ bushels of corn ‘cost 253 cents, what will one 


bushel cost ? Ans. 46 cents. 
38. If 61 bushels of wheat cost 1025 cents, what will 
one bushel cost ? Ans. 164 cents. 
39. If 164 yards of cloth cost 5350 cents, what will 
pne yard cost ? Ans. 828 cents. 
40. If 562 pounds of tea cost 2951 cents, what will one 
pound cost ? Ans. 52 cents. 
41. If 691 barrels of flour cost 69500 cents, what will 
one barrel cost ? Ans. 1000 cents. 


42. If you can buy 101 yards of muslin for one dollar 
for how many dollars could you buy 2394 yards? 
Ans. $228. 
43. if one yard of silk cost 873 cents, how many yards 
may be bought for 8575 cents? 
Ans. 98 yards. 


REDUCTION. 31 


44. If one pound of tea cost 332 cents, how many 


pounds may be bought for 21715 cents ? 
Ans. 645 pounds. 


45. If one dollar will buy 132 pounds of sugar, how 
many dollars will buy 1875 pounds ? Ans. $100. 


FEDERAL MONEY. 


Arr. 62. What is Feprrat Monry ? 


Federal Money is the currency or money of the United 
States, and consists of Hagles, Dollars, Dimes, Cents, and 


Mills. 


10 Mills (m.) Make 1 Cent, Marked ct. 
10 Cents ss 1 Dime, d. 
10 Dimes or 100 cents “ pe WL VUE CE a BS. $. 
10 Dollars ; be Eagio ee, 


Art. 63. What is Reduction of Federal Money ? 


It is the changing of Federal Money from one denomina- 
tion to another without altering the value. 


Art. 64. To reduce dollars to cents, 


Ruie.—Multiply the dollars by 100, and if there be 
cents, add them in. 


Notr.—In writing dollars and cents, if the cents consist of one figure, 
prefix a cipher to the cents, and if there are dollars and cents, or dollars, 
cents and mills expressed in the same number, prefix the sign of dollars 
to the whole amount, and after the dollars place a point; the first figure 
to tho right of the point will be dimes, the second, cents, and the third, 
mills, the first two figures to the right of the point, taken together will be 
cents, and the three taken together will be mills. 


Arr. 65, To reduce cents to dollars, 


Rurze.—Divide the cents by 100; the quotient will be 
dollars and the remainder cents ; the result must he written 
as the previous note directs. 


32 FEDERAL MONEY. 


Notr.—If the given number be mills, cut off three figui2s to the right b7 
means of a point, and prefix to the whole the sign for dollars. If the given 
number be dollars and cents, the whole will be reduced to cents by omitting 
the point, and if there be dollars, cents, and mills, omit the point and the 
whole will be reduced to mills. 


1. Reduce $7 to cents. Ans. 700 cents. 
2. Reduce $18 to cents, Ans. 1800 cents. 
3. Reduce $6.25 to cents. Ans. 625 cents. 
4. Reduce $54.645 to mills. Ans. 54645 mills. 
5. Reduce $35.05 to cents. Ans. 3505. cents. 
6. Reduce $17.09 to mills. Ans. 17090 m. 
7. Reduce $53.405 to mills. Ans. 58405 m. 
8. Reduce 47 cents to mills. Ans. 470 m. 
9. Reduce $95.007 to mills. Ans. 95007 m. 
10. Reduce 496 cents to dollars. Ans. $4.96. 
11. Reduce 584 cents to dollars. Ans. $5.84. 


12. Reduce 1609 cents to dollars. Ans. $16.09. 
13. Reduce 14327 mills to dollars. Ans. $14.327. 
14. Reduce 150 cents to dollars. Ans. $1.50. 
15. Reduce 520 mills to cents. Ans. 52 cts. 
16. Reduce 98006 mills to dollars. Ans. $98.006. 


ADDITION. 


Art. 65, To add Federal Money, 


Ruie.—Place dollars under dollars, cents under cents, 
dc., add as in simple numbers, and place a point in the 
amount under the points in the sum. 


1, What is the sum of $6.50, $8.96, $5.12, $17.63, 
$91.40, and $16 2 Ans. $145.61. 
2. What is the sum of $75.19, $63.54, $3.06, $9.25, 
$65.37, $416.12, $375, $600, and $5 ? 
Ans. $1612.53. 
3. What is the sum of $861.55, $378.25, $461.37 
$683.57, $728.39, $460.08, and $17 ? 
Ans. $3590.21. 


SUBTRACTION. 33 


4. What is the sum of $18.50, $3780, $658.06, 
$358.653, $818,047, $67.375, and $486.395 2 
Ans. $6187.03. 
5. What is the sum of $398.007, $5.65, $885.307, 
$43.936, $729.063, $335.72, $8316.472, $3768.082 and 
56 cents 2 Ans. $14482.797. 
6. What is the sum of $3000, $1616.05, 375 mills, 
$387.50, $38456.087, $4900.008, and $2500. 
Ans. $15860.02. 
7A person bought a house for $5000, a store for 
$6290, merchandise foe $23654.12, a horse and wagon 
for $978.53, a farm for $9371.60, rail-road stock for 
$11500, and a watch for $92.725; what did the whole 
amount to 2 Ans. $56186.975. 


SUBTRACTION. 
Art. 66. To subtract Federal Money, 


Rurz.—Place the less quantity under the greater, with 
dollars under dollars, cents under cents, dc. ; subtract as 
in semple subtraction, and place a point in the remain- 
der under the points of the minuend and subtrahend. 


. From $75.67 take $47.35. Ans. $28.32. 
. From $378.91 take $257.66. Ans, $121.25. 
. From $835.06 take $286.09. Ans. $548.97. 
. From $1865.72 take $394.88. Ans. 1470.84. 
. From $6958.375 take $1400.75. 
Ans. $5557.625. 
. From $18397 take $9508.44. Ans. $8888.56. 
. From $23467.06 take $15729.489. 
(ANB roti | Ls 
8. From the sum of $981.43 and $456.81, take 


~t OUR 09 Oe 


$498.79. Ans. £939, 49. 
9, From $10,000 take the sum of $4367.18 and 
_ $3587.47. Ans $2045.35. 


10. From the sum of $965 and $341.60, take the sum 
of $433.83 and $89.47. Ans. $783.80. 


34 FEDERAL MONEY. 


1], A person at various times received $27.40, 
$68.75. $810.47, $386.59, $2.20; he also paid the fol- 
lowing amounts: $78.67, $129.72, $119.46, and $3.88 ; 
how much did he have left ? Ans. $963.68. 

12, A person had $50000; he bought a horse and wagon 
for $550, which he sold for $625; he then bought a house 
_ for $3750, and built a store which cost $7875, and bought 

groceries to the amount of $1895.63 ; how much did he 
then have left ? Ans. $36554.37. 


MULTIPLICATION. 
Art. 67, To multiply Federal Money, 


Rurz.—Multiply the given amount of Federal Money 
by the multiplier, as in simple multiplication ; the product 
will be of the same name as the given amount of Federal 
Money. 


1. Multiply $586 by 13. Ans. $7618. 
2. Multiply $28.50 by 15. Ans. $427.50. 
3. Multiply $381.45 by 24. Ans. $9154.80. 
4, Multiply $299.66 by 39. Ans, $11686.74. 
5. Multiply $75.867 by 73. Ans. $5538.291, 
6. Multiply $492.25 by 160. Ans. $78760. 
7. Multiply $4971.80 by 28. Ans. $139210.40. 
8. Multiply $659.375 by 32. Ans. $21100. 
9 


. Multiply $1875.125 by 54. Ans. $101256.75, 


When the value of a single article is known, how can the value 
of any number of articles of the same kind be found? (Art. 84.) 


10. If one barrel of flour cost $6.75, what will 29 
barrels cost ? Ans. $195.75. 
11. If one barrel of pork cost $13.88, what will 100 
barrels cost ? Ans. $1388. 
12. If one barrel of beef cost $15.75. what will 139 
barrels cost ? Ans. $2189.25. 
13. If one hogshead of wine cost $287.40, what will 
17 hogsheads cost ? Ans. $4885.80. 


MULTIPLICATION. 35 


14. If one cord of wood be worth $9.625, what will 


278 cords be worth ? Ans. $2675.75. 
15. If one acre of land cost $488.69, what will 625 
acres cost ? Ans. $805431.25. 


16. If it cost the United States $109688.15 a day, for 
the expenses of government, how much will it amount 
to in 865 days ? Ans, $40036174.75. 

17. A person bought 561 pounds of cheese at 15 
cents a pound, and 398 pounds of coffee at 17 cents a 
pound; how much was the whole? Ans, $151.81. 

18. A flour merchant sold 291 barrels of flour at 
$7.20 a barrel, 2961 bushels of corn at 54 cents a bushel, 
and 398 bushels of rye at 78 cents a bushel; how much 
did the whole cost ? Ans, $4004.58. 

19, A merchant had $21000; he bought 500 yards 
of cloth at $3.75 a yard, 354 yards of silk at $1.125a 
yard, and 37 pieces of linen, each piece 16 yards, at 94 
cents a yard; how much money had he lett ? 

Ans. $18170.27. 

20. A bought 48 tons of iron, at $64.28 a ton, and 
39 tons of copper, at $193.50 a ton; B bought 633 bar- 
rels of flour, at $6.60 a barrel, and 1000 bushels of oats, 
at 73 cents a bushel; how much more money did A 


spend than B ? Ans. $5724.14. 
(21.) 
New York, Aug. 1, 1850. 
JouN JONES | 
Bought of Avery Wuirs, 
31 Dozen Buttons - - - at 25 cents a dozen. 
49 “* Pairs of Gloves “ 78 ‘“ a dozen pairs, 
133 Spools of Cotton - - “ 7 “ aspool. 
389 Papers of Needles- - “ 8 “ a paper. 
198 Pairs of Combs - - “ 16 “ a pair. 
627 Papers of Pins - - sala -“ “a paper. 


en imeem 


What is the total ? $205.86. 


36 FEDERAL MONEY. 


(22. ) 
New York, July 3d 1853. 


TimotHy JENNINGS 
Bought of Envwarp DURAND, 


461] Yards o£ Clothy. w-yf-),ated4i25s 6 yard. 
329 66 Silk = a n 66 a 17 66 
BAS Sa Santini ce 15 yO. ORS esha 


DAS an Hine. Cassimere is: 9 wos Tas Be 
397 66 66 De Laine i. “6 1.475% & 


What is the total ? $4965.505, 
(23.) 
Find the amount of the following bills: 


Sold Cuar.es Ricwarps, 


10 Yards Striped Cassimere at $2 
RA TCHS g va aL 20 
5.“ Bins BF ES DADS 


Ans, $388.75, 


(24.) 
Sold Joun W. Hearn, 


12 Yards Blue Broadcloth at $3.50 
3 Pieces 110 yds. Sheeting “ 20 cts. 
9 Yards Black Broadcloth- “ 4.50 

50°) * Blacksbrints sear - ao. 31 cts. 


Ans. $164.00 
(25.) 
Sold Cuar.es Smit, 


10 Pieces 64 yds. Bleached Shirtings at 20 cts. 
15” 3 eae 2° a Sheetings “ 26 “ 
16“ 66 “ Kentucky Jeans - “ $1.15 


Ans. $1584.20 


DIVISION. a7 


(26.) 

Sold James C. Hunt, 

o4 Yards Black Broadcloth at $6 

B40 4S8 ADtickwe: =) = '= cme 183 
AS tise Blues erints SS 239. oe 25 
10 Dozen Coat Buttons’ - «= - .§ 52 
68 Yards Fancy Cassimere - - - “ $1.50 
1002 ahs Blue use ae teed DAE DY 
64 “ Black Prints nits tee oY O14 

Ans. $400.24. 
DIVISION. 


Arr. 68. To divide Federal Money, 


Rutzt.—Divide the given amount in Federal Money by 
the divisor, as in semple divison. 


When the number of articles and their value are known, how can 
the value of a single article be found? (Art. 53.) 


When the value of a single article and the value of several 
articles are known, how can the number of articles be found? 
(Act. 54.) 


NotEe.—In this case the divisor and dividend must be of the same name; 
that is, if the divisor or dividend be cents, the other must be brought to cents 
likewise; or if either be mills, the other must be brought to mills. 


1. Divide $1728.42 by 6. Ans. $288.07. 
2. Divide $18672.96 by 24, Ans. $778.04. 
3. Divide $1432.64 by 37. Ans. $38.72, 
4. Divide $2099.334 by 219. Ans. $9.586. 
5. Divide $28221 036 by 372. Ans, $75.863. 
6. Divide $639.88 equally between 17 men. 


Ans. $37.64 per man. 
7%. If one hundred acres of land cost $3759.60, what 


will one acre cost ? Ans. $37,596. 
8. If 390 yards of silk cost $487.50, what will one 
yard cost ? Ans. $1.25. 


4 


38 FEDERAL MONEY. 


9. If 275 acres of land ccst $87752.50, what will one 
acre cost ? Ans. 319,10. 

10. If a person earn $6314.50 in 3865 days, how much 
can he earn in one day ? Ans. $17.80. 

11. If 346 barrels of flour cost $1825.150, what will 
one barrel cost ? Ans. $5,275. 


NorrE.—in finding the value of a single article, if the dividend consist of 
dollars only and there should be a remainder, annex two ciphers io the 
dividend, and continue the division to two more figuresin the quotient, which 
two figures will be cents; if there be a remainder then, annex one more 
cipher to the dividend and continue the division to one more figure in the 
quotient, which will be mills. 


12. If 125 barrels of flour cost $650, what will one 


barrel cost ? Ans. $5.20. 
13. If 32 gallons of wine cost $68, what will one 
gallon cost ? Ans, $2.125, 
14. If 96 yards of cloth cost $552, what will one yard 
cost ? Ans. $5.75, 
15. If 375 yards of cloth cost $2154, what will one 
yard cost? Ans. $5,744, 
16. If 224 cords of wood cost $3984.56, what will one 
cord cost ? Ans. 17.565. 
17. If 320 bushels of oats cost $264, what will one 
bushel cost ? Ans. 825 mills. 
18. If 576 pounds of tea cost $482, what will one 
pound cost ? Ans. 75 cents. 
19. If 700 gallons of oil cost $567, what will one 
gallon cost ? Ans. 81 cents. 
20. At 6 cents a piece, how many pine-apples*can be 
bought for 72 cents ? Ans. 12, 
21. How many acres of land can be bought for 
$87725 at $275 an acre 2 Ans. 319. 
22. At $5.27 per barrel, how many barrels of flour 
ean be bought for $50065 2 Ans. 9500 barrels. 
23. Ifa barrel of apples cost $2.50, how many barrels 
can be bought for $175? Ans, 70. 
24. Ifa yard of satin cost $3.50, how many yaras can 
be bought for $315 ? Ans. 90 yards. 


25. At 875 mills a bushel, how many bushels of rye 
can be bought for $148.75 ? Ans. 170. bushels, 


PROMISCUOUS EXAMPLES, 39 


26. If one pound of tea cost 54 cents, how many 
pounds may be bought for $1852 Ans. 250 pounds. 


PROMISCUOUS EXAMPLES. 


1. If 16 horses cost $2560, what will 1 horse cost at 
the same rate? Whatwill 7 horses cost? Ans. $1120. 
2. If 212 pounds of tea cost $161.12, what will 1 
pound cost ? What will 13 pounds cost ? Ans. $9.88. 
3. If 56 acres cf land cost $16657.20, what will 385 
acres cost ? Ans. $10410.75, 
4. If 311 bushels of wheat cost $855.25, what will 
160 bushels cost ? Ans. $440. 
5. If 429 bushels of wheat cost $847.49, what will 
2000 bushels cost ? Ans. $1620. 
6. If 19 lots cost $18738.75, what will 38 lots cost ? 
Ans. $37477.50. 
7. If 196 pounds of butter cost $49, what will 2500 
sak cost ? Ans. $625 
. If 2000 yards of muslin cost $1180, what w vill 
1699 yards cost ? Ans. $961.11. 
9. ]f29 yards of cloth cost $101.50, how many yards 
can you buy for $122.50? Ans. 35 yards. 
10. If 150 yards of cloth cost $751.50, how many 
yards can be bought for $125.25 ? Ans. 25 yards, 
11. Hf a person can earn $1181.25 in 225 days, how 
many days would it take him to earn $1764 ? 
Ans. 336 days. 
12. If 86 hogsheads of sugar cost $6815.12, how 
many hogsheads « can be bought for $21927.50 ? 
Ans. 125 hogsheads. 
18. If 23 tons of iron cost $1730.75, how many tons 


may be bought for $9632 ? Ans. 128 tons. 
14. If 108 equal lots of ground cost $5711.04, how 
many would $1322 buy 2? Ans, 25 lots. 


15. If 325 acres of land cost $17712.50, how many 
acres can be bought for $545 ? Ans, 16 acres, 


40 TABLES OF WEIGHTS AND MEASURES. 


16. If 8160 barrels of pork cost $48032, hcw many 
barrels can be bought for $1170.40 2 
Ans. 77 barrels. 
17. If 4129 barrels of flour cost $26219.15, how much 
will 360 barrels cost ? Ans. $2286. 
‘ 18. If 8 pieces of cloth, each piece 35 yards, cost 
$996.80, what will be the price of 26 yards ? 
Ans. $92.56. 
19. A person had $15000; he bought 30 bales of 
cotton, each bale 940 pounds, at 10 cents a pound; he 
paid $6680 for a house, and spent the remainder in flour, 
at $5.50 a barrel; how many barrels did he get ? 
Ans. 1000 barrels. 


TABLES OF WEIGHTS, MEASURES, &o. 


Art. 69.—ENGLisH or Strertinc Money. 


4 Farthings make 1 Penny, abbreviated d. 
12 Pence : 1 Shilling . &. 
20 Shillings “ 1 Pound * £., 


Norr.—A sovereign is of the same value asa pound. A guineais valaed at 
21 shillings. 


Farthings are abbreviated thus :— 


dd. One farthing. 
4d. Two farthings. 
éd. Three farthings. 


Art, 70.—Troy Wetaur. 
24 Grains (gr.) make 1 Pennyweight, abbreviated Tut. 


20 Pennyweights “ 1 Ounce, 02. 
12 Ounces 7) 1 Fou » 1b. 


What is the use of Troy Weight ? 
Troy Weight is used to weigh jewels, gold, silver, and 
liquors. 


TABLES OF WEIGHTS AND MEASURES. 41 


Art. 7].—Avotrpuporis WEIGHT. 


16 Drams (dr.) make 1 Ounce abbreviated oz. 
16 Ounces 1 Pound : 16 
25 Pounds “ 1 Quarter = qr. 
4 Quarters “ 1 Hundred weight, = cwt, 
20 Hundred weight. “ 1 Ton, - L: 


What is the use of Avoirdupois Weight ? 


Avoirdupois Weight is used to weigh coarse goods, such 
as groceries, and the metals, excepting gold and silver 


Norr.—5760 grains make one pound Troy; 7000 grains of tne same king 
make one pound Avoirdupois. 


Art. '72,—APporTHecaries’ WEIGHT. 


20 Grains (gr.) make 1 Scruple, abbreviated %. 


3 Scruples : 1 Dram, . 3. 
8 Drams a 1 Ounce, * S's 
12 Ounces - 1 Pound, 4 Th. 


What is the use of Apothecaries’ Weight ? 


Apothecaries’ Weight is used to mix medicines. 


Art. 73.—Ciotra MEAsuRE. 
2+ Inches (i2.) make 1 Nail, abbreviated na. 


4 Nails iy 1 Quarter, - gr. 

4 Quarters - 1 Yard, yd. 

8 Quarters % 1 Ell Flemish, “ LE. Fi. 
5 Quarters 4 1 Ell English, “ LE. E. 
6 Queters % 1 Ell French, “ LE. Fr 
175 Yards - 1 Metre, bs 

1b che ds « 1 Aune, cs 


What is the use of Cloth Measure? . 


Cloth Measure is used to measure Dry Goods, Rib 
bons, &c. 


‘Notr.—French and German goods are generally invoiced by metres oa 
aunes. 
4* 


42 TABLES OF WEIGHTS AND MEASURES. 


Art. 74.—Lone MEAsure. 


12 Inches (in.) make 1 Foot, abbreviated, ft. 

3 Feet - © «ad Yeards : yd. 

54 Yards fo welel Od, s0l Olea rd.or p 
40 Rods “ 1 Furlong, iy fur. 

8 Furlongs set eal FUN fe m. 

3 Miles “«~ .1 League, “ d 

69 Miles (statute) “ 1 Degree of the equator. 

60 Miles (geographic) “ 1 Degree of the equator. 
860 Degrees “ 1 Circumference of the earth. 


What is the use of Long Measure ? 


Long Measure is used to measure distances, heights 
depths, dc. 


Art. 75.—Lanp or SQuaRE MEASURE. 


144 Square Inches (sq. zn.) make 1 Square Foot, ab'd. sq. ft. 


9 Square Feet 1 Square Yard, 8g. Yd. 
80} Square Yards “ 1 Square Rod or pole, “ saat Rs 
40 Square Poles “~ 1 Rood, ke. 
4 Roods *, 51 Acre, aA 
640 Acres am tba Square Mile, “ 8g. m. 


What is the use of Land or Square Measure ? 


Land or Square Measure is used to measure land or 
the surface of anything that has length and breadth. 


NotE.—When length and breadth are multiplied together, the product 
‘epresents a surface. 


Arr. 76.—Soiip or Cusic Measure. 
1728 Cubic Inches (sol. or cv. in.) make 1 Cubic Foot, ab’d. cu. ft 


27 Cubic Feet 1 Cubic Yard, “ cw, Ps 

40 Cubic Feet “ 1 Ton Round Timber, fea is 

50 Cubic Feet “ 1 Ton Hewn Timber, 7: H. 

42 Cubie Feet “ 1Ton of Shipping, 7. 
128 Cubie Feet “ 1 Cord of Wood, C. 


Note -A Cord of Wood is 8 feet long, 4 feet wide, and 4 feet high. 


What is the use of Solid or Cubic Measure 2 


Solid or Cubic Measure is used to estimate the solia 


TABLES OF WEIGHTS AND MEASURES, 


43 


contents of bodies that have length, breadth, and thickness, 


such as timber, stone, &c. 


Note.—-When length, breadth, and thickness are multiplied together, the 


vioduct represents a solid. 


Art. 77.—CircutarR MEasure. 


60 Seconds () “ 1 Minute, abbreviated =” 
60 Minutes “ 1 Degree, “ i 
30 Degrees Sed) Olen, bs & 
12 Signs or 860 degrees make 1 Circle, e ¢. 
Art. 78.—Wine Mzasoursz. 
4 Gills (gi.) make 1 Pint, abbreviated, pt. 
2 Pints Z Quart, * gt. 
4 Quarts “1 Gallon, * gal. 
314 Gallons base aa! Barrel, 2 bbl. 
63 Gallons “1 Hogshead, He hhd. 
2 Hogsheads “ 1 Pipe, s pt. 
2 Pipes “al, Bad WF ee tun, 


NoTE.—231 cubic inches make onesgallon wine measure. 


Art. 79.—Brrr Measure. 
2 Pints (pt.} make 1 Quart, abbreviated, gt. 


4 Quarts se 1 Gallon, + gal, 
36 Gallons us 1 Barrel, es bbl. 
54 Gailons & 1 Hogshead, + hhd 


NotE —282 cubic inches make one gallon beer measure. 


Arr. 80.—Dry Measure. 
2 Pints [pé.] make 1 Quart, abbreviated, qt. 


8 Quarts 1 Peck, pk. 
4 Pecks by 1 Bushel, = bu. 
8 Bushels ~ 1 Quarter, _ gr. 
32 Bushels « 1 Chaldron, £ ch, 


4 
Note.—21507 6 cubic inches make one bushel. 


Art. 8].—Time. 


60 Seconds (sec.) iy 1 Minute, abbreviated, 
60 Minutes . 1 Hour, = 
24 Hours 1 Day, “ 
7 Days i 1 Week, > 
4 Weeks s Lunar month, - 
12 Calendir months “ Year, ~ 
8652 Days 4 Year - 


44 TABLES OF WEIGHTS AND MEASURES. 


Art. 82,—MisceLuanzous TABLE. 


12 Units make 1 Dozen 
12 Dozen or 144 § 1 Gross. 
a2(grossor 1728. “ 1 Great gross. 
20 Units 2 1 Score. 
56 Pounds od 1 Firkin of butter 
100 Pounds “ 1 Quintal of fish. 
200 Pounds * 1 Barrel of beef or pork, 
» 200 Pounds “ 1 Barrel of shad or salmon. 
196 Pounds “ 1 Barrel of flour. 
M used to measure the 
ee 1 Hand ; height of horses, 


used for measuring tke 
6 Feet 1 Fathom, + length of cordage and 
depth of water 


24 Sheets of paper “ 1 Quire. 
20 Quires a 1 Ream. 
2 Reams ~ 1 Bundle, 
10 Bundles S 1 Bale. 
&, 
Surveyor’s Mrasure. 
73°25 Inches make 1 Link. 
25 Links | 1 Rod. 
100 Links “ 1 Chain. 
80 Chains _ 1 Mile. 


Loca, CurRENCIES OF THE UNITED STAtTEs. 


8 Shillings make $1 in N. Y., N. C., Ohio, and Michigan. 


6 “+* $1 in Ne Bea. Ky, Tenn., Ta., HL, Mi., and Mo, 
74 ¢ *-*  $19n Pemba. JE Del., and Md. 
4s, 8d. = $1 in Ga. and §. C. 


Tn the other states Federal Money is generally used: 5 shillings 
of Canada or Nova Scotia money make $1 United States: and 
4s, 6d. sterling is the nominal value of $1 U.S. 


REDUCTION.—DENOMINATE NUMBERS, 


Art. 83, What is Repuction. 


Reduction is the changing of a quantity from one de 
nomination to another without altering the value. 


DENOMINATE NUMBERS. 45 


Art. 84. How many kinds of reduction are there ? 


Two kinds: Reduction Ascending and Reduction 
Descending. 


Art. 85, What is Reduction Descending ? 


Reduction Descending is the changing of a quantity 
from a higher to a lower denomination. 


Art. 86. What is Reduction Ascending ? 


Reduction Ascending is the changing of a quantity from 
a lower to a higher denomination. 


Art. 87. To reduce a denominate number from 8 
higher to a lower denomination, 


Rute.—Multiply the highest denomination of the given 
quantity by as many of the denomination next lower as 
will make a unit of that denomination, and add in the 
next lower denomination if there be any: multiply this 
result as before, and so proceed until the whole is reduced 
to the denomination required. 


Art, 88. To reduce a denominate number from & 
lower to a higher denomination, 


Ruiz.—Divide the given quantity by as many of its 
own denomination as will make aunit of the denomination 
next higher ; divide this result as before, and so proceed 
until the whole is reduced to the denomination required ; 
if there be remainders they will be of the same denomina 
tion as the divisor or dividend. 


EXAMPLES——-STERLIYG MONEY. 


1. Reduce £14 to shillings and pence. 
: Ans. 280s. 33860d. 
2. Reduce £255 to shillings and pence. 
Ans. 5100s. 61200d. 
3. Reduce £3472 to shillings and pence. } 
Ans. 69440s. 882280d. 


4h 


REDUCTION, 


4, Reduce £120 5s. to shillings. 


Ans. 2405s. 


5. Reduce 36s. 93d. to farthings. 


Ans. 1766 farthings, 


6. Reduce £1126 13s. 4d. to pence. 


Ans. 270400d. 


7. Reduce £985 83d to farthings. 


Ans. 945685 far. 


8. Reduce 15s. 81d. to farthings, 


Ans, 753 farthings. 


9. Reduce 1806 pence to shillings. 


Ans. 150s. 6d. 


10. Reduce 4896 shillings to pounds. 


11: 
12. 
13. 
14. 


15. 
16. 
17. 
18. 
19, 


20. 
21. 


22. 


Ans. £244 16s. 
Reduce 16454 pence to pounds. — 
Ans. £68 11s. 2d, 
Reduce 40033 pence.to pounds, 
Ans. £166 16s. 1d. 
Reduce 877 farthings to shillings. 
Ans. 18s, 34.d 
Reduce 176455 farthings to pounds. 
Ans. £183 16s. 13d. 


TROY WEIGHT. 


How many pennyweights in a pound ? 
Ans, 240 dwt. 
How many grains in a pound ? 
Ans. 5760 grains, 
Reduce 245 pounds to ounces, 
Ans, 2940 cunces, 
Reduce 18 lb. 6 oz. to dwt. 
Aus. 4440 dwt. 
Reduce 11 0z. 16 dwt. to grains, 
Ans. 5664 gr. 
Reduce 614 lb. to grains, Ans, 3536640 gr. 
Reduce 23 lb. 7 oz. 19 dwt. to grains, 
Ans. 136296 gr, 
Reduce 61 lb. 13 dwt. 16 gr. to grains, 
Ans, 351688 gr, 


DENOMINATE NUMBERS. 


. Reduce 4560 dwt. to ounces. Ans. 243 oz. 
. Reduce 9818 dwt. to pounds. 


Ans. 40 lb. 10 oz. 18 dwt. 


. Reduce 7815 oz. to pounds. 


47 


Ans. 651 Ib. 3 oz. 


. Reduce 96388 grains to pounds. 


Ans. 16 Ib. 8 oz. 16 dwt. 4 gr. 


. Reduce 386245 grains to pounds. 


Ans, 67 Ib. 0 oz. 18 dwt. 13 gr. 


Ans. 100 lb. a cwt. 2000 lb. a ton. 


. How many ounces make a quarter, cwt., and to 


Ans, 


Ans, 


. Reduce 75 tons to pounds. Ans. 150000 lb. 
. Reduce 15 cwt. 3 qr. 21 Ib. to pounds. 


Ans. 1596 Ib. 


. Reduce 14 Ib. 18 dr. to drams. 


Ans. 8597 dr. 


. Reduce 13 T. 3 qr. 19 lb. to drams. 


Ans. 6680064 dr. 


. Reduce 44 ewt. 1 qr. 12 oz. to drams. 


Ans. 1182992 dr, 


. Reduce 2560 drams to pounds. 


Ans. 10 Ib. 


. Reduce 2598 lb. to cwt. 


Ans, 25 cwt. 3 qr. 23 Ib. 
Reduce 15724 dr. to cwt. 
Ans. 2 qr. 11 lb. 6 oz. 12 dr 


. Reduce 55200 lb. to tons. 


Ans, 27 T. 12 ewt. 


. Reduce 18608129 drams to tons. 


Ans. 36 T. 6 ewt. 3 qr. 13 Ib. 1 dr, 


. Reduce 1000000 ounces to tons. 


Ans. 31 T. 5 owt. 


. How many quarters make a ton? Ans. 80. 
AVOIRDUPOIS WEIGHT. 
. How many pounds make a ewt. and ton? 


n? 


. How many drams make a quarter, cwt., and ton? 


48 DENOMINATE NUMBERS. 


APOTHECARIES’ WEIGHI1. 


43. How many 3 make a pound ? Ans, % 3 
44, How many scruples make an % and Ib. ? 
Ans. 24 5 inan 3 7 288 D inalk 
45. How many grains makea 3, 3, and Ib. ? 
Ans. 60 gr. ina 3, 480 gr.ina % ,5760 gr. inalh 
46. Reduce 472 lb. to 3. 
Ans, 453123. 
47, Reduce 38 lb. 6 %,33,2 5D, to grains. 
Ans. 221980 gr. 
48, Reduce 7 3,1 9, 12 gr. to grains. 
Ans. 3392 gr. 
49. Reduce 3676 3 to pounds. 
Ans. 38 lb. 3 3,4 3. 
50. Reduce 78611 gr. to pounds. 
Ans. 121b. 0.2 723.7% Di Or 
51. Reduce 1000000 gr. to pounds. 
Ans. 178 Upto 5 258 so hs 
52. Reduce 79 lb. 3 3,1 3,1, 15 gr. to gr. 
Ans. 456575 gr. 


CLOTH MEASURE. 
538. How many nails ina yard. (Art. 59.) 


Ans. 16 na 
54. How many inches in a yard ? Ans. 36 1n. 
55 Reduce 27 yards to nails, Ans, 432 na. 
56. Reduce 15 E, E. to nails, Ans. 300 na. 


57. Reduce 30 E. E. to inches. (Art. 59.) 
Ans. 1350 in 
58. Reduce 293 E. Fr. to inches. Ans. 15822 in, 
59. Reduce 1753 na. to E, Fr. 
Ans. 73 E. Fr., 1 na 
60. Reduce 7412 in. to yards. (Art. 61.) 
Ans. 205 yd. 3 qr. 2 na. 2 in 
61, ee 3298 in. to E. E. 
Ans. 73 E. E. 1 qr. 1 na, 12 in 
62. Renee 1411 in. to E. Fr. 
Ans.26 E, Fr. 0 qr. 3 na. } in 


66 


REDUCTION. 49 


LONG MEASURE. 


. How many furlongs make a degree ? 


Ans. 556 fur. 


. How many rods make a degree and a mile ? 


Ans, 22240 rd. in a deg. and 320 rd. in a m. 


. How many yards make a degree and a mile? 


Ans, 122320 yd. ina deg. and 1760 yd. in am. 
How inany inches make a mile ? 
Ans. 63360 in. 


. How many inches in 79 yards. Ans, 2844 in, 
68.. 


How many rods in 73 miles ? 
Ans. 23360 rd. 


. How many inches in 15 yd. 7 in. 


Ans. 547 in. 


. Reduce 1m. 3 fur. 27 poles to poles. 


Ans. 5907 p. 


. Reduce 16 dest 19 m. 3 fur. to rods. (Art. 59.) 


Ans. 362040 rd. 


. Reduce 37 fur. 11 rods to inches. 


Ans. 295218 inches. 


. Reduce 145 miles to feet. Ans. 765600 fect. 
. Reduce 19 m. 5 fur. 12-p. 3 yd. to feet. 


Ans. 103827 feet. 


. Reduce 79 deg. 41 m. to inches. 


Ans. 350475840 inches. 


. Reduce 1277 inches to yards. 


Ans. 35 yd. 1 ft. 5 in. 


. Reduce 4006 poles to miles. 


Ans. 12 m. 4 fur. 6 p. 


. Reduce 176 yd. to rods. Ans. 32 rods. 
. Reduce 1478 statute miles to degrees. 


Ans, 21 deg. 13 m. 4 fur. 


. Reduce 11492 in. to furlongs. 


Ans. 1 fur. 18 rd. 8 in. 


. Reduce 4000000 ft. to miles. 


Ans. 189 m 8 far. 6rd. 1 ft, 


. Reduce 753689 yd. to degrees. 


Ans, 6 deg. 11 m. 1 fur. 34 rd. 2 yd 
5 : 


50 DENOMINATE NUMBERS. 


&3. Reduce 7706160 ft. to degrees. 
Ans. 20. deg. 69 m, 4 fur, or 21 deg, 


LAND OR SQUARE MEASURE, 


84. Reduce 18 acres to square poles. 
Ans. 2880 sq. p. - 
85. In one square mile how many roods ? 
Ans. 2560 roods. 
86. How many square rods make a square mile ? 
Ans. 102400 sq. rd. 
87. How many square feet make an acre ? 
Ans. 43560 sq. ft. 
88. Reduce 450 square yards to square inches. 
Ans. 583200 sq. in. 
89. In18 A. 8R.15 sq. p., how many square yards, 
Ans. 670033 sq. yd. 
90. In 144 sq. m. 54 A. 28 sq. p., how many square - 
poles ? 
Ans. 14754268 sq. p. 
91. In 37 roods, how many square inches ? 
Ans. 58021920 sq. in. 
92. Reduce 13796 sq..in. to square yards, 
Ans. 10 sq. yd. 5 sq. ft. 116 sq. in. 
93. Reduce 196441 square poles to square miles, 
Ans. 1 sq. m. 587 A. 3 R. 1 sq. p. 
94. Reduce 7800 Pa: ft. to square rods. 
s. 28 sq. rd. 19 sq. yd. 6 sq. ft. 
95, Reduce 20000000 square feet to acres. 
Ans. 459 A. 21 sq. p. 262 sq. yd. 2 sq. ft., or 459 
A. 21 sq. p. 26 sq. yd. 8 sq. ft. 108 sq. in. 
96. A piece of ground is 50 yards long and 25 yards 
wide, how many square yards are there in the surface ? 
Ans. 1250sq. yd. 
97. One side of a square box is 3 ft. long and 2 ft 
high, how many square ee are in the four sides? 
Ans. 24 sq. ft. 


REDUCTION, 5] 


SOLID OR CUBIC MEASURE. 


98. In 1 cord how many solid inches ? 
Ans, 221184 cu. 1p. 
99. Reduce 4 tons of round timber to cubic inches, 
Ans. 276480 cu. in. 
100 Reduce 7 tons of hewn timber to cubic inches, 
Ans. 604800 cu. in. 
101. In 4866 cubic feet, how many cords? 
Ans. 38 ¢. 2 cu. ft, 
102. In 1847629 cubic inches, how many tons of 
round timber ? Ans, 19,7, 19. cu, ft..1517 cudin. 
103. In 44 tons round timber and 18 solid feet, how 
many cubic inches ? Ans. 3063744 cu. in. 
104. In 256 cu. yd. 15 cu. ft. 1000 cu. in., how many 
cubic inches ? Ans. 11970856 cu. in. 
105. In a box 5 feet long, 4 feet wide and3 feet high, 
how many solid feet ? Ans. 60 solid ft. 


LIQUID MEASURE. 


106. Reduce 1 tun to quarts. Ans. 1008 qt. 
107. Reduce one hogshead to gills. 
Ans, 2016 gi. 
108. Reduce 6 barrels to gills. Ans, 6048 gi. 
109. Reduce 55 gal. 3 qt. 2 gi. to gills. 
Ans. 1786 gi 
110. Reduce 14 pipes, 76 gal. 1 pt. to pints. 
Ans, 14721 pt. 
111. Reduce 315 hhd. 29 gal. 1 pt. to gills. 
Ans. 635972 gi, 
112. Reduce 13000 pints to hogsheads. 
Ans. 25 hhds. 50 gal. 
113. Reduce 17867 gills to barrels. 
Ans. 17 bbls. 22 gal. 3 qt. 3 gi. 
114. Reduce 11002 gal. to barrels. 
Ans, 3849 bbl. 8 gal. 2 qt. 
115. Reduce 71561 pt. to tuns, 
Ans. 35 T. 1 hhd. 62 gal. 1 pt. 
116, Reduce 17598 pints to barrels, beer measure. 
Ans. 61 bbl. 3 gal. 3 qt. 


52 


117, 
118. 


119. 
120. 
“al2; 
122. 


123. 


124, 


125, 
126. 


127. 
128. 
129. 
130. 
181. 
182. 


Jays. 


133. 


134. 
135. 


DENOMINATE MUMBERS. 


DRY MEASURE, 


Reduce 1 bushel to pints. Ans. 64 pt. 
Reduce 13 bu. 2 pk. 7 qt. to quarts. 
-Ans. 439 qt. 
Reduce 9 ch, 23 bu. to pints. Ans, 19904 pt. 
In 16751 pt., how many bushels ? 
Reduce 4001 pecks to chaldrons. 
Ans, 31 ch. 8 bu. 1 pk. 
Reduce 18757 qt. to chaldrons. 
Ans. 13 ch. 13 bu. 3 pk. 5 qt. 
In 34 ch. 5 bu. 3 pks. 7 qt., how many quarts ? 
Ans. 35007 qt. 


TIME. 


Reduce 365 da. 6 hr. or one year to hours. 
Ans. 8766 hr. 
Reduce a century to days. Ans. 36525 days. 
In one week, how many minutes ? 
Ans. 10080 min. 
In one year, how many minutes ? . 
Ans. 525960 min. 
Reduce 5 yr. 78 da. 11 hr. to hours. 
Ans, 45593 hr. 
Reduce 7 wk. 2 da. 14 hr. to minutes. 
Ans. 74280 min. 
Reduce 7300 hr. to weeks. 
Ans. 43 wk. 3 da. 4 hr. 
Reduce 179963 seconds to days. 
Ans. 2 da. 1 hr. 59 min. 28 see. 
Reduce 86875 hours to years, each year 3654 
Ans. 4 yr. '75 da. 11 hr. 
Reduce 67981861 min. to centuries, 
Ans. 1 cent. 29 yr. 92 da. 9 hr. 1 min. 


CIRCULAR MEASURE. 
Reduce a circle to minutes and seconds. 
Ans. 21600 min. 1296000 sec. 
Reduce 8 signs to minutes and seconds. 
Ans. 5400 min. 324000 see. 


REDUCTION. 53 


136. Reduce 16° 31’ 30” to seconds. Ans. 59490”, 
137. Reduce 7 signs 29° 11’ to seconds. 
Ans, 861060”, 
138. Reduce 360060” to degrees. Ans. 100° 1’, 
139. Reduce 700000” to signs. 
Ans, 6 signs 14° 26’ 40”, 
140. In 496820’, how many circles ? 
Ans. 23 cir. 20’, 


PROMISCUOUS EXAMPLES. — 


1. In 7 quires of paper, how many sheets ? 


Ans, 168. 
2. In 14 barrels of beef, how many pounds ? 
Ans. 2800 Ib. 
3. The depth of a river is 17 fathoms: how many 
inches is that ? Ans, 1224 in. 
4. A horse is 174 hands high; how many inches is 
that ? Ans, 70 inches. 


5. How many sheets in a ream of paper ? 
Ans. 480 sheets. 
6. If 3416 lbs. of butter are to be put in firkins of 
56lb. each, how many firkins will be required ? 
Ans, 61 firkins. 
7. A person wishes to pack 16 head of cattle, which 
average 3000 lb. each of packing beef; how many bar- 
rels, each containing 200 Ib., will he require ? 
Ans. 240 barrels. 
8. How many pens in 85 gross? Ans. 5040 pens, 
9. How many buttons in 568 gross ? 
Ans. 81792 buttons. 
10. What is the price of 18cwt. 3qr. 161b., at 2 


cents a pound ? Ans. $37.82. 
11. A hhd. of sugar weighs 11 ewt. 2 qr. 261b.; what 
will it cost, at 7 cents a pound ? Ans, $82.32. 


12. If a room is 18 feet long, and 16 feet wide, how 
rauch will it cost to carpet, at $1 20 per square yard ? 


Ans. 38.40. 
5* 


54 DENOMINATE NUMBERS. 


13. How many bottles, each holding 1 pt. 3 gi. will 
be required to bottle 3 pipes of wine ? 
‘Ans. 1728 bottles, 
14, How long is a piece of ground which is 64 yd, 
wide and contains 176 acres ? Ans. 13310 yd. 
15. A pile of wood is 8 feet high, 4 feet deep, and 
168 feet long ; what will it be worth at $7 a cord? | 
Ans. $294. 
16. How many yards of flannel, 1 yd. 2 qr. wide, will 
line a cloak 2 yd. long and 6 yd. wide ? 
Ans. 8 yd. 
17. How many spoons, each weighing 2 oz. 13 dwt., 
can be made from a lump of silver weighing 2 lb. 10 oz, 
9 dwt? Ans. 13 spoons. 
18. A person owes £168 13s. 104d; he gives 20 bar. 
rels of flour, each worth £2 10s. 6d., and the rest in 
money ; how much money must he pay ? 
Ans. £118 3s. 102d. 
19. I want to bottle 15 gallons of wine in an equal 
number of quart and pint bottles; how many of each 
must I have ? Ans. 40 qt. and 40 pt. bottles. 
20. Divide 16 barrels of flour, each weighing 196 lb., 
into 20 parcels of 14 lb. each, and the rest into parcels 
of 7]lb. each; how many of these latter parcels are 
there ? Ans. 408 parcels. 
21> Divide a hhd. of sugar containing 1400 lb. into 
an equal number of parcels, of 18, 10, and 7 each; how 
many will there be ? Ans. 40 of each, 
22. How many bottles does it take to put 165 gal. 
1 pt. 1 gi. into bottles holding 1 pt. 3 gi. each? 
Ans. 755 bottles. 
23. A Jeweller has 7]b. ll oz. 1 dwt. 20 gr. which 
he wants to make into spoons; 10 spoons, each 2 oz. 11 
dwt. 14 gr; 25 spoons, each 1 oz. 4 dwt., and the rest 
into spoons, each 1 oz. 12 dwt. 18 gr; how many are 
there of this last weight ? Ans. 24 spoons. 
24. A person has 18 cwt. 3qr. of sugar, worth § 
cts. a pound, which he exchanged for cloth at $5 per 
yard ; how much cloth did he get? Ans. 80 yd. 


REDUCTION OF CURRENCIES, 55 


REDUCTION OF CURRENCIES. 


Azar. 89. To reduce Federal Money to the various. 
State currencies. 


Rou.e.— Multiply the given amount of Federal Money 
by the value of $1, expressed either in shillings or pence ; 
tf the sum contain cents, divide the product by 100 ; or tf 
tt contain mills, divide the product by 1000, and the quo- 
tient will always be of the same denomination as that in 
which the value of $1 ts expressed. 

Notr.—<£. s. d., with the various divisions of « dollar into shillings and 
penny were employed in keeping accounts in the States, previous to the Revo- 


ution, and they are still used to a limited extent. In those States, whose 
names are not down in the table of currencies, Federal Money only is used. 


1. In $59, how many pounds New York currency ? 
r Ans. £23 12s. 

2. In $279.75, how many pounds New York cur- 
rency ? Ans. £111 18s. 

3. Reduce $4861.275, to pounds New York currency. 
Ans. £1944 10s. 23d. 

4, Reduce $61.75 to pounds New England currency. 
Ans. £18 10s. 6d, 

5. In $581.15, how many pounds New Jersey cur- 


rency ? Ans. £217 18s. Tid. 

6. How many pounds, South Carolina currency, in . 
$2813.665 ? Ans. £656 10s. 54. 

7. Reduce 75 cents to shillings, New England cur- 
rency. Ans, 4s, 6d. 


8. How many pounds, New England currency, will 
275 barrels of flour cost, at $5.50 a barrel ? 
Ans, £453 15s, 
9. How many pounds, Pennsylvania currency, will 
1760 bushels of wheat cost at 924 cents a bushel ? 
Ans. £610 10s. 
10. What will be the price, in pounds, New York 
currency, of 5 hhds. of sugar, each weighing 1321 lbs., 
at 7 cents a pound ? Ans. £184 188. 93d. 
11. How many pounds, South Carolina currency, will 


56 REDUCTION OF CURRENCIES. 


pay for 13 T. 15 cwt. 28 lbs. of iron at 41 cents a 
pound ? Ans. £289 Os. 104d. 
12. How much money, Canada currency, will pay for 
755 bushels of wheat, valued at $1.20 a bushel ? 
Ans. £226 10s. 


Art. 90. To reduce the various State Currencies to- 
Federal Money. 


Ruizt.—Divide the given amount by the value of $1, 
both reduced to the same denomination, the quotient will 
be dollars ; multiply the remainder, if any, by 100 and 
continue to divide, in order to obtain the cents, dc. 


13. In £25, New York currency, how many dollars? 


Ans. $62.50. 
14. How many dollars in £15 4s., New York cur- 
rency ? Ans. $38. 
15. Reduce £186 13s. 9d., New York currency, to 
Federel Money. Ans. $466.72 (nearly.) 
16. In £759 16s. 8} South Carolina currency, how 
much Federal Money ? Ans, $3256.44. 
17. Reduce £992 15s. 7d., Pennsylvania currency, to 
Federal Money. Ans, $2647.41. 
18. Reduce 3s. 5d., New England currency to Federal 
Money. Ans. 57 cents (nearly.) 
19. How many dollars and cents in £211 8s. 10d., 
Canada currency ? Ans. $845.77. 
20. In £296 13s. 4d., New Jersey currency, how 
many dollars and cents ? Ans. $791.11. 


21. Reduce 51s. 74d., Virginia currency to Federal 
Money. Ans. $8,465. 


ADDITION. 57 


DENOMINATE NUMBERS.—ADDITION. 


Axt. 9]. To Add Denominate Numbers. 


Ruize.— Write the numbers with the like denominations 
under each other ; commence at the column of the lowest 
denomination, add it up, and if the sum be less thana 
unit of the next higher denomination, set it down under the 
column added ; if it be more than a unit of the next higher 
denomination, reduce it to tre next higher denomination, 
place the remainder under the column added, and carry 
the quotient to the column of the next higher denomination ; 
proceed with each column in the same manner to the last, 
the total amount of which must be set down. 


(1.) (2.) 8) 


La s.b a: Suels  Sae. £ ar ae. 
Add 17 ao § 145 0 91 487 12 1+ 

184.4; .9 169 Lies 399 15 “7 

LT CG 175 14 7 456 1 1i¢ 

29 18 9 166 15 83 798 19 81 

LG Le 3S 1199 5 10 100 «st0) 1 

99 9 1856 14 7 2242 17 93 

(4.) (5.) 

fb. oz. dwt. lb. oz. dwt. gr. 

196 11 19 986 Ae eS fei Lil 

44 6 16 GSaio el a! 

55 10 15 AA ale pO 216 

144 9 8 2S Ul A 5 

169 5 2 6 9 1 14 


GIT Ress 0 1395 «0 «11 «(412 


(6. 


cwt. 
16 
11 
19 
6 
1 
15 


11 


— 
se 
— 


oF 
ON 


is 
~ 
 comiil aeneed 


DOO DEH OOS 


) 


DENOMINATE NUMBERS, 


qr. 


TWP OINO Ho uw 


su) ®~ CO R=! CO ~ 


5 


Wwmwr war 


=O OW WH LY 


(7.) 
ewt.. qr. Ib. oz 
iD 2G aaaeo 
9438 6 6 
88 1 15 I1 
3 1 24 10 
900-3 LO 3 
44 1 20 2 


(9.) 


on 
ROR CIVIAWA A 
Om Ue Oe woe U 


ADDITION, 


(12.) 


29 


Ca CR COR On| 


peal 
GO 
nr 


Pwo) 
eo) 
meow wor s 


=) 
te 


(13.) 
Vem t bene 273: 
na) ray CaM 
68 1 10 
G2, Ape fe! ah 
fig cra} 1 
14 2 10 
Dien om O 
19ecl-e 8 
1Gyp. «9 
(15.) 
deg. m. fur. 
28 59 5 
22 38 6 
41 58 7 
Iie>38 1 
ot 2 
76 53 4 
1 41 83 
188 69 4 
184 
(17.) 
8q. rods. sq. yd. sq.ft. sq. in. 
19 eide 8S. lid 
4 25 8 126 
198 15 2 100 
Oo) 8S 7 
Oe i2z. 5) 6 RD 
243 121 6 85 


59 


60 


15 
2019 


DENOMINATE NUMBERS. 


— 


ol DK wner @ 
ee 


8q. Pp. sq. yd. 
30 15 


ib? 11 
31 16 
29 30 
18 26 


6 oh 


Oe HO eS 


— tS et eS 


(19.) 


5q. yd. sq. ft. sq. im, 
96 1 


"Ms 
15 
ee! 
28 


JFOOU | 
for) 
for) 


(21.) 
sol. yd. sol. ft. sol. in 
18 24 1600 
29 14 1706 
188 13 497 
54. 19 296 


496 15 1081 


LGS sels 


861 12 


ADDITION. 61 


(26.) (27.) 
W. da hr. yl. mo. da. 
3 6 14 17 5 20 
17 4 20 1G* ee 
39 2 16 LIZ ~¢ FON 
2. 6 = 5 it ed 4 
gS 1 23 5 10 21 
28.) (29.) 
sigas, 8° ’ @ ’ ” 
2° 4 50 50 37 50 12 
3) Poo be 4I 1HVehES 21 
1 25 44 46 IGNV1O? 29 
18 35 36 4 54 16 
24 11 49 Uiie2? a5 


4 5 wW 55 6 47 35 


30, A person owes several sums of money; to one 
17s. 6d.; to another, £3 5s. 8d.; to another, £25 11s. 
101d.; to another, £12 8d.; to another, 16s. 33d. ; to 
another, £126 4s.; to another, £31 6s, 104d.; to 
another, £50 4s. 43d. What is the whole amount ? 

Ans. £250 7s. 31d. 

31. A person has 5 pieces of ground; the first con- 
tains 16 A. 3 R.; the second, 17 A. 1 R. 1 sq. p. 45 
sq. feet; the third, 11 A. 14 sq. p. 62 sq. feet; the 
fourth, 2 A. 3 R. 120 sq. ft.; and the fifth, 41 A. 2 R. 
7 sq. p. What is the amount of the whole ? 

Ans. 89 A. 1 R. 22s8q. P. 227 sq. ft. 

32. Off of one field of wheat were raised 37 bu. 1 pk. 
3 qt.; of a second field, 41 bu. 2 pk. 5 qt.; of a third, 
25 bu. 1 pk. 3 qt.; of a fourth, 43 bu. 3 pk. 1 qt. How 
much was the whole ? Ans. 158 bu. 4 qt. 

6 


62 DENOMINATE NUMBERS. 


33. A person travelling, goes 26m. 3 fur. 12 rd., the 
first day ; 28 m. 5 fur. 9rd. 9 ft. the second day; 31 m. 
ldrd. 14 ft. the third day; 26m. 7 fur. 12 ft. the fourth 
day ; and 33m. 7 fur. 16rd. 11 ft. the fifth day. How 
far does he go during the 5 days? 

Ans. 146 m. 7 fur. 14rd. 15 ft. 

34. A jeweller receives on one day 11 1b. 602. «f 
gold; on another day, 10 1b. 50z. 20 gr.; on another. 
6oz. 3dwt. 16 gr.; on another, 51lb. 17 dwt. 1 gr.; 

on another, 16 Ib. 4.0z. 15 dwt. 15 gr. How much does 
he receive in all ? Ans. 48 lb, 10 oz. 17 dwt. 4 gr. 

35. A grocer received an invoice of 7 hhd. of sugar ; 
the first weighed 11 cwt. 15 1b.; the second, 12 ewt. 3 
gr. 15 1b.; the third, 9 cewt. I qr. 161b.; the fourth, 12 
ewt. 1 qr.; the fifth, 11 ewt. 3 qr. 241b.; the sixth, 9 ewt. 
24 1b.; the seventh, 138 cwt. How much did the seven 
hogsheads contain ? Ans, 79 cwt. 3 qr. 19]b. 


os 


SUBTRACTION. 
Art. 92. To Subtract Denominate Numbers. 


Rute.— Write the like denominations of the subtrahend 
under those of the minuend ; commence at the lowest 
denominator, and subtract the lower number from the one 
above, and set down the remainder under that denomina- 
tion; uf the number below be more than the one above, add 
to the upper number as many of its own denomination as 
it takes to make a unit of the next higher, and from the 
sum take the number below ; ‘set down the difference, ane 
carry one to the under number of the next higher denomt. 
iation, and proceed with it as before. 


(1.) (2.) 
; Diesel bie £ $e 
From 17 13 9 1918 11 8} 
Take 18 17 6 819 6 91 


o 16 3 1099 4.112 


Se 


tons 


15 


cwt. qr. 


75 16 3 
74 19 2 


SUBTRACTION, 


woo} 


Ib. OZ. 


14 14 
11 15 


Ib. oz. 


114 3 
91 4 


cwt. qr. 


tebe dw 


Pap eal 


p. 
162 2535; 12 
6 


(4.) 


dwt. gr. 


16 12 


Ll D 


(6.) 


idem OZ. aie 


16 2 
PAV | 


19 


So 


63 


DENOMINATE NUMBERS. 


(13. (14.) 
Deg. m. fur. Deg. m. fur rd 
110 49 2 16 69. 235200 
43 60 3 15: 69526 gaLs 
66 574 7 or 68i 5 3 or 
66 58 3 COM LE 3 
(15.) (16.) 
6q. Mm. A. i ET A.) Reesd.ups Sq-1y0- 
1386 410 3 20 75 2 14 11 
11 182 2 19 7 i end HH Ee Hs 
hash ake pi? 
(17.) (18.) 
sq. yd. sq. ft. sq. in. C. CU. ite ecu in. 
ee LO, 178 112 1689 
GariMe skew 41 125 13898 
(19.) (20.) 
soi. yd. sol. ft. sol. in. Ding) CaLerates pt, 
37 15 1000 167706 2ae 
6 25 1307 LG Pee Gir aa | 
(21.) (22.) 
ey eal. sgt, Spt. vel. ch. bu. pk. qt 
ee164415. 1°83 TT oe 
4 200 21 8 98 25 Foes 
Ooo. 0 -O 16-20-63] 


cones ue 


SUBTRACTION. 65 


(23.) (24.) 
yr. mo. da. yr. mo. da. 
1845 7 12 Hyg tht) gy 4 
1882 8 20 1789 4 19 
(25.) (26.) 
W. da hr. min. seo. C. sign. © < y 
44 1 20 16 48 Poem 0s Orn, 
99 1 23 11 «59 8 12 49 59 
(27.) 
sign, 0 y ” 
Tig 14 169-29 


4 25 46 24 


28. A person owes £78 3s, 21d.; he pays £17 17s. 
13d.; how much does he still owe ? 
Ans. £60 6s. 01d. 
29. A owes B for 2 invoices of merchandise; one 
worth £17 16s. 81d., the other £11 2s. 9d.; he pays 
£25 16s, 4d. ; how much does he still owe? 
Ans. £3 3s. 11d. 
30. A farmer has a farm consisting of 200 acres. He 
gave his eldest son 109 A. 3 R. 20 sq. P.; to his second 
son, 48 A. 1 R.; the remainder he gave to his third son. 
What was the remainder? 
Ans. 41 A. 3 R. 20.sq. P. 
31. In the previous sum how much more did tho 
eldest receive than the third son? Ans. 68 A. 
32. What is the length of time between January 16th, 
1812, and February 11th, 1840 ? 
Ans. 23 yr. 25 da. 
6* * 


66 DENOMINATE NUMBERS. 


83. What is the difference in time between August 
13th, 1750, and January 16th, 1841? 
Ans, 90 yr. 5 mo. 3 da. 
34. How long is it ffom July Ist, 1852, to March 


17th, 1853 2 Ans, 20 yr. 8 mo. 16 da. 
35. How long is it from June 21st, 1811, to Decem- 
ber 14th, 1815? Ans 4 yr. 5 mo, 23 da. 


36. The latitude of New York is 40° 42’ 40”, of 
Quebec 46° 50’ 10’; how many degrees is Quebec north 


of New York? Ans. 6° 7’ 30”, 
37. The latitude of Boston is 42° 21’ 22’’; how far is 
Boston from the North Pole ? Ans, 47° 38’ 38”. 


38. A merchant bought 8 pieces of cloth; the first 
measured 47 yd. 3 qr. 1 na.; the second, 43 yd:; the 
third 41 yd. 3 qr. 8 na.; when he came to examine it, 
he found 18 yd. 3. na. worthless ; how much good cloth 


was there ? Ans. 119 yd. 2 qr. 1 na. 
39. From 16 deg. 69 m. 3 fur., take 15 deg. 69 m. 
6 fur. 12 p. Ans. 69 m. 0 fur. 28 p. 


40. Out of a hhd. of tobacco weighing 13 cwt. 3 qr., 

there were sold 8 cwt. 2 qr. 11 1b. ; how much was left ? 
Ans. 5 cwt. 0 qr. 14 Ibs. 

41, What was the value of the remainder at 9 cts, 
per pound ? Ans. $46.26. 


MULTIPLICATION. 


Arr. 93, To Multiply Denominate Numbers, 


Ruie.—Place the multiplier under the lowest denomina- 
tion and multiply it by the multiplier ; reduce the product t 
the next higher denomination, and carry the quotient to th 
product of the next higher denomination by the same mul- 
tiplier ; proceed in like manner to the highest denomina: 
tion, when the whole product must be set down. 


1. Multiply £17 18s. 6d. by 7. Ans, 125 9s. 6d. 
2. Multiply £296 13s. 91d. by 12. 
Ans. 3560 5s. 8d. 


MULTIPLICATION. 6” 


. Multiply 38 lb. 6 oz. 17 dwt. by 17. 
Ans. 655 Ib. 8 oz. 9 dwt. 
. Multiply 19 T. 13 ewt. 2 qr. 18 Ib. by 19. 
Ans. 373 T. 19 ewt. 3 qr. 17 Ib. 
. Multiply 3 lb.4% 23 15 17¢r. by 11. 
Ans. 36 lb. 113% 43 25 Ter. 
. Multiply 61 E. Fr. 5 qr. 1 na. by 8. 
Ans. 495 KE. Fr. 
. Multiply 15 yd. 1 ft. 11 in. by 21. 
Ans, 328 yd. 1 ft. 3 in. 
. Multiply 17m. 2rd. 16 feet. by 23. 
Ans. 391 m. 1 fur, 28rd. 5 ft. 
. Multiply 15rd. 2 yd. 1 ft. by 29. 
Ans. 447 rd. 1 yd. 2 ft. 
10. Multiply 144.A.3R.17 sq. p. 19 sq. yd. by 5. 
Ans. 724 A. 1 R. 8 sq. p. 43 sq. yd. 
11. Multiply 17 C. 59 cu. ft. 718 cu. in. by. 13. 
Ans. 
12. Multiply 73 hhd. 61 gal. 3 qt. 1 pt. by 26. 


oOo DO 4 O&O.’ & © 


Ans. 
13. Multiply 14 bu. 3 pk. 4 qt. by 37. 


Ans. 
14. Multiply 38 cent. 19 yr. 360 da. by 14., 3651 days 
to the year. Ans. 534 cent. 79 yr. 2913 “da. 


15. Multiply 18° 40’ 41” by 53. Ans. 

16, Multiply 18 bu. 3pk. 5 qt. ape 72. 
Ans. 

17. Multiply £114 11s. 21d. by 36. 
Ans. 

18. Multiply 4 deg. 17 m. 5 fur. by 36. 
Ans, 

19. Multiply 49 yd. 1 ft. 11 in. by 29. 
Ans, 

20. Multiply 18 bbl. 20 gallon 2 qt. by 37, 

ns. 

21. Multiply 17 w. 4 da. 11 hr. 16 min. by 1381. 
Ans. 

22. Multiply 1 A. OR. 11sq. p. by 149, 


Ans. 


68 DENOMINATE NUMBERS. 


23. Multiply 39 cwt. 3 qr. 15 1b. 2 0z, 13 dr. by 4? 
Ans, 

24. Multiply £7 18s. 6d. by 389. 
Ans. 

25. Multiply 15 lb. 7% 3 3 by 678. 

, Ans, 

26. Multiply 22 lb. 8 oz. 13 dwt. 21 gr. by 981. 

Ans. 


27. Multiply $47.29 by 711, according to this rule 
Ans. 

28. Multiply 17 gal. 2 qt. 1 pt. 3 gi. by 819. 
A 


ns. 


When the value of a single article is known, how can the volae 
of any number of articies of the same kind be found? (Art. 34.) 

When it is Enown what can be bought for 1 dollar or 1 pound, 
how is the qnantity that can be bought for any number of dollars 
or pounds found ¢ 

Multiply the quantity that can be bought for one dollar or pound 
by the number of dollars or pounds. 


29. If one cord of wood cost £1 16s. 94d., what will 
25 cords cost ? 
Ans, £45 19s. 91d. 
30. If you can buy 3 bu. 2pk. 3 qt. for one dollar, 
how many bushels can be bought for $79 ? 
. Ans, 283 bu. 3 pk. 5 qt. 
31. Bought 17 yards of lace, at £3 17s. 1d. per yard; 
14 yards of crape, at £2 10s. per yard. What is the 
value of both purchases ? 
Ans. £100 10s. 5d. 
32. If you buy 13 yd. 3 qr. 2 na. for £1, how many 
yards can be bought for £38 ? 
Ans. 527 yd. 1 qr: 
3. If you can exchange one acre of wheat for 17 A. 
3 R. 7 sq. p. of pasture, how many acres of pasture can 
you get for 41 acres of wheat? Ans. 729 A. 2 R.7 sq. p. 
34, Bought 16 pieces of lace, each containing 62 yd., 
at £1 11s, 2d. per yd., and sold 7 pieces for £1 15s. per 
yd., and the rest at £1 13s. 10d. per yd. ; how much w4 
gained ? Ans, £157 Ils 84. 


DIVISION. 69 


35. Bought the following bill of goode : 


Bt ds 
20 lb. Butter at 2 9 per ib. 
10 lb. Cheese “ 1 33 & 
100 lb. Sugar “ 9 $5 
30 lb. Tea ft ey brote) 
What is the total amount ? 
Ans, £18 12s, 11d. 
(36.) 
Bought of SHepuErp, & Co., 
ab a ph ya e hs 
46 Barrels Om POrkn Lata on Lane ae per barree. 
49 CO ISOCL ak dened A Lanai Aedes 
144 i louraa a co wel me eS caiteer a 
56 : “ Fish WG hn ok BRA a 
LO Fee Gee OUT esa  d, Wal OF Wan) aia ee 
What is the total amount ? 
Ans, £1448 12s. 3d, 
(37.) 
New York, April 17, 1853. 
Bought of Jonzs & Co., 


eid 
SOC ARCS b-minaice eng, Sod eeet: Guns Cacle. 
14 Doz. Hooks - “% 38 O per doz. 
129% HGGs t-te fins gt 1 6 each. 
PEA ANE TER ee NG fier ex 
68 Hammers - - “ 3 2 each. 


75 Screw-drivers - ‘“ ly Osa 
16 Gross of Screws “ 14 51 per gross. 


i, iekeaxes) Fe. - 1 “os 1 San Raieach: 
W hat is the amount of the bill 2 
Ans. 
DIVISION. 


Art. 94, To Divide Denominate Numbers, 


Ru.e.—Divide the divisor into the highest denomination 
of the dividend, and set the quotient under that denomina: 


mu 


wir ; 


DENOMINATE NUMBERS. 


reduce the remainder to the next lower denominution 


and add in as many as there are of that denomination, 
and divide the sum by the divisor, set down the quotient 
and proceed with the remainder as before ; of there should 
be no remainder, divide the divisor into the next lower 


denomination. 
1. Divide £91 12s. 6d. by 6. Ans. £15 5s. 5d. 
2. Divide £168 19s. 23d. by 19. 
| Ans, £8 17s. 101d. 
3. Divide 386 Ib. 0 0z. 16 dwt. 23 gr. by 29. 
Ans. 13 Ib. 3 oz. 15 dwt. 148. 
4, Divide 9 tons 16 cwt. 2 qr. 16 lb. 3 oz. 4dr. by 
Pee Ans. 11 ewt. 2 qr. 6 lb. 13 oz. 51% dr. 
5. Divide 61 lb, 103,453,005, 16 gr. by 36. 


6 
7 
8. 
9. 


Ans. 1 lb.8 3,553,095, O18 or. 


. Divide 129 E.E. 4 qr. 1 na. 2 in. by 63. 


Ans. 2 E.E. 0 qr. 1 na.+ 


. Divide 78 m. 8 fur. 14 p. by 31. 


Ans, 2m. 4. fur. 9 p. 
Divide 4 yd. 1 ft. 11 in. by 15. 
Ans. 0 yd. 0. ft. 1152, in. 
Divide 1986 m. 3 fur. 20 p. 1 yd. by 108. 
Ans. 18 m. 8 fur. 5 p. tyo3 yd. 


10. Divide 86 deg. 60 m. 3 fur. 19 p. by 121. 


11. Divide 224 A. 3 R. 17 sq. p. “ 22, 


Ans. 49 m. 7. fur. 6,83- p. 


121 


Ans. 10 A. 0 R. 85 54 sq. p. 


12. Divide 284 sq. yd. 8 sq. ft. 120 sq. in. by 79. 


Ans. 3 sq. yd. 5 sq ft. 67 44 sq. in, 


sof 


13. Divide 19861 sq. m. 179 A. 3 R. 20 sq. p. 
1] sq. yd. by 61. 


Ans. 325 sq. m. 380 A. 2R. 24 sq. p. 182 sq. yd. 


14 Divide 738 cu. yd. 20 eu. ft. 1190 eu. in, by 399, 


Ans. 1 cu. yd. 22 eu. ft. 17 18333 cu. in. 


15. Divide 158 cords, 111 sol. ft. 1250 sol. in by 


310. 


Ans, 65 cu. feet, 1085 8% cu. in. 


16. Divide 20 hhd. 16 gal. 3 qt. I gi, by 147. 


Ans. 8 gal. 2 gt. 1 pt. 1433 gi 


DIVISION. 71 


17. Divide 175 bu, 3 pk. 1 qt. 1 pt. by 67. 
Ans. 2 bu. 2 pk. 3 qt. 182 pt. 
18. Divide 1 circle by 128. 2° 48’ 45”, 
19. Divide 365 da. 6 hr. by 240. 
Ans. 1 da, 12 hr. 31 min. 30 see. 


When the value of a single article and the value of a number of 
articles are known, how can the number of articles be found! 
(Art. 54.) 

When the number of articles and their value are known, how 
can the value of a single article be found? (Art. 53.) 


20. If 16 bushels of oysters cost £75 17s. 4d., what 
will one bushel cost ? Ans. £4 14s, 10d. 
21. If 24 barrels of apples cost £98 16s., how much 
will one barrel cost ? Ans. £4 2s, 4d. 
22. If 200 acres of land cost £13390, what will one 
acre cost ? Ans. £66 19s. 
23. If you can buy 359 bu. 1 pk. 4 qt. of apples for 
£100, how many bushels can you buy for one pound ? 
Ans. 3 bu. 2 pk. 3 qt. 
24. If one yard cost 2s. 6d., how many yards can be 
bought for £180 ? Ans. 1440 yd. 
25. If you can buy 15 sq. rods of land for £1, for how 
many pounds can you buy one acre ? 
Ans. £10 13s. 4d. 
26. Divide a square mile into 15 equal parts. 
~ Ans. 42 A. 2K. 26 sq. p. 20 sq. yd. 1 sq. ft. 72 sq. in, 
27. A man travelled 1249 m. 5 fur. 36 rod in 61 
days; how far did he travel in a day ? 
Ans. 20 m. 3 fur. 36 rd. 
28. A cartman carried 117 cords, 110 cu. ft. in 100 
loads; how much did he average a load ? 
Ans. 1 C, 22 cu. ft. 1486 785 cu. in. 
29. A tailor had two pieces of cloth; one was 29 yd. 
3qr. long, and the other 31 yd. 1 qr. 1 na. long; he 
made 3 coats out of the first piece, and one out of the 
second; it took 8 yd. 2 qr. to make each coat; how 
many yards of cloth had he left out of the two pieces ? 
Ans. 47 yd. 0 qr. 1 na. 
30. A man bought 6 pieces of cloth, each piece 34 yd, 


72 DENOMINATE NUMBERS. 


2 qr.; afterwards he bought 11 pieces, each 35 yd. I qr. 
3 na.; he sold 296 yd. 2 qr. out of the whole; how 
much had he left ? Ans. 300 yd. 1 qr. 1 na. 

31. A person had £1000; he had two sons and three 
daughters; he gave each son £280 3s. 9d., and divided 
the remainder equally among the daughters. How ~ 
much did each daughter get ? 

Ans. £146 10s. 10d. 

32. A gentleman owns 3 farms; the first contains 49 
A. 3 R. 18 sq. p.; the second, 94A.1R. 28 sq. p., and 
the third 146 A. 34 sq. Dp. He divided it into 20 equal 
portions, 8 of which he kept for himself, and the rest he 
divided equally between his 4 children; how much did 
each child receive ? Ans. 43 A. 2 R. 12 sq. p. 

33. There are 2 men, who have 179 A. 3 R. 16 sq. p. 
divided equally between them; the first divides his share 
equally between his 3 children, and the second divides 
his-equally between his 2 children; how much does a 
child of each receive ? 

Ans. $29 A. 3 R, 36 sq. p. for a child of Ist. 

44 A.3 R. 34sq.p. “ e 2d. 
34, If 3 yards of cloth cost £4 16s. 6d., how much 


will 12 yds. cost ? Ans. £19 6s. 
35. If 16 acres of land be worth £260 10s. 8d., how 
much will 80 acres cost ? Ans. £488 10s. 
36. If 138 cwt. of sugar cost £54 18s. 6d., what will 
4 cwt. cost ? Ans. £16 18s. 
37. If 389 head of cattle cost £1891 10s., what will 17 
cost 2 Ans. £824 10s. 
38. If 75 barrels of flour cost £164 10s. 71d., what 
will 30 barrels cost ? Ans. £65 16s. 3d. 


39. If the cost of transporting a block of marble 7 
miles is £3 5s. 4d., how much would it cost for 3 miles? 


Ans, £1 8s. 
40. If 47 yards of velvet cost £156 18s. 23d. what 
will 100 yards cost ? Ans. £333 17s. Id. 


41. A person at his death left a house worth £1191 
2s. 9d; 2 farms worth £1726 each; furniture worth 
£629 11s., and money to the value of £2860 18s. 9d, 


DIVISION. 713 


which was equally divided among his 5 sons; what was 
the share of each son? Ans. £1626 14s. 6d. 
42. If 767 A. 2 R. be equally divided between 100 
men, how much will 54 of them get. 
Ans. 414 A. 1 R. 32 sq. p. 
43. If 7 gross of buttons cost £2. 16s., how much will 
100 gross cost? - Ans. £40. 
44. A brewer sold 9 hhd. of beer, each of which con. 
tained 53 gal. 2 qt. 1 pt.; 18 gal. leaked out of the 
whole; he sold another lot of 16 hhd., each containing 
54 gal. 1 qt., out of which there leaked 21 gal. 1 qt., 
how much remained out of both sales ? 
Ans. 1311 gal. 1 qt. 1 pt. 
45. A person travelling at the same rate every day, 
goes 175 m..3 fur. 25 p. in 5 days; how far does he go 
in 87 days? Ans. 1298 m. 2 fur. 33 rd. 
46. If a quantity of provisions will last 64 men for 3 
wk. 5 da., how long will it last one man? 8 men ? 
Ans. 29 wk. 5 da. 
47. A man left property to the amount of £1718 9s. 
6d.; he divided this into 2 equal parts, one of which he 
gave to his wife, and the other part was divided equally 
between his 3 daughters; how much did each daughter 


get, and the wife ? 
hee £859 4s. 9d., for wife. 
"* | £286 8s. 3d. for each daughter. 
48, At the beginning of the year 1852, a grocer laid 
in 17 hhd. of sugar, each weighing 11 ewt. 2 qr. 15 |b. ; 
7 casks of cheese, each cask weighing 19 ewt. 1 qr..12 
lb. ; 40 chests of tea, each weighing 60 lb. He took an 
account of stock at the beginning of 1853, and found on 
hand 126 cwt 3 qr. 14 lb. of sugar, 98 ewt. 1 qr. ot 
cheese, 32 chests and 28 Ib. of tea; how much sugar 
cheese, and tea had he sold? 
71 ewt. 0 qr. 16 lb. of sugar. 
Ans. 4 387 cwt, 1 qr. 9 lb. of cheese, 
} 452 Ib. tea, 


74. INTRODUCTION TO FRACTIONS. 


INTRODUCTION TO FRACTIONS. 


Art. 95, What is a Common Divisor of two or more 
Numbers 2 


It is a number which wiil divide them all without a 
remainder. 


Art. 96. What is the greatest Common Divisor of 
two or more Numbers ? 


It is the greatest number that will divide each of them 
without a remainder. 


Arr. 97. To find the greatest Common Divisor of 
two Numbers, 


Ruiz.— Divide the lessnumber into the greater ; if there 
be a remainder, divide it into the previous divisor, and so 
proceed until there is no remainder ; the last divisor wile 
be the greatest common divisor of the two numbers. 


1. Find the greatest common divisor of 126 and 729. 
Ans. 9. 

2. Find the greatest common divisor of 144 and 729. 
Ans. 9. 

3. Find the greatest common divisor of 720 and 1296. 
Ans. 144. 

4, Find the greatest common divisor of 225 and 1260. 
Ans, 45, 

5. Find the greatest common divisor of 432 and 1728. 
Ans. 482. 

6. What is the greatest common divisor of 3136 and 
4096 2 Ans. 64. 

7. What is the greatest common divisor of 457 and 
831 ? Ans. I. 

8. What is the greatest common divisor of 444 and 
wer ie Ans. 111. 


INTRODUCTION TO FRACTIONS. 7h 


Art. 98, To Find the greatest Common Divisor of 
more than two Numbers, 


Rutu.—JLind the greatest common divisor of two of 
them ; then take this common divisor and another of the 
given numbers and find their greatest common divisor ; 
the last divisor will be the greatest common divisor of the 
three numbers ; if there be more, proceed in the same way. 


9. Find the greatest common divisor of 720, 1296, and 


1944. Ans, 72. 
10. What is the greatest common divisor of 525, 625, 
and 700 ? Ans, 25. 
11. What is the greatest common divisor of 360, 648, 
and 972? Ans. 36. 
12. What is the greatest common divisor of 56, 140, 
and 182 ? Ans. 14. 
13. What is the greatest common divisor of 175, 245, 
- and 343? Ans. 7. 
14. Find the greatest common divisor of 576, 864, 
1028, and 1296. Ans. 4. 
15. What is the greatest common divisor of 512, 
1280, 1920, 2720, and 3440? Ans. 16, 
16. What is the greatest divisor of 198, 343, and 1716 2 
Ans. 1. 


Art. 99, What is the Common Dividend or Multi- 


‘le of two or more Numbers ? 

It is a number which can be divided by all the given 
wumbers without a remainder. 

Art. 100. What is the least Common Dividend or 
Multiple of several Numbers ? 

Lt is the least number into which all the given numébers 
can be divided without a remainder. 


ART. 101. To find the least Common Dividend of 
several Numbers, 


Ruie.— Arrange the given numbers in a horizontal row ; 


76 INTRODUCTION TO FRACTIONS. 


reject those numbers that are exact divisors of any one of 
the others, then divide the numbers not rejected by any 
prime number thut will exactly divide two or more of them, 
bringing down those that cannot be divided exactly, in the 
same line with the quotients ; then reject any of these num- 
bers that are exact divisors of another, and divide the 
numbers nut rejected as before, and so proceed until no 
prime number will divide two or more of the numbers in 
the last row ; the product of the numbers in this row and 
of all the divisors will be the least common dividend of the 
given numbers ; or, 

Separate each number into its prime factors, and reject 
all the common factors except one; the product of the 
factors not rejected, will be the least common dividend. 


Norte.—If the numbers are prime, their product will be the least common 
dividend. 


17. Find the least common dividend of 4, 8, 12, 16, 20. . 


Ans, 240. 
18. Find the least common dividend of 5, 15, 24, 27, 
40. Ans. 1080. 
19. What is the dividend of 8, 10, 15, and 18 ? 
Ans. 360. 
20. What is the common dividend of 4, 12, 16, and 
19? Ans. 912. 
21. What is the least common dividend of 3, 6, 9, 12, 
15, and 18? Ans. 180. 
22. What is the least common dividendof 2, 4, 7, 6, 8, 
and 10? Ans. 840. 
23. What is the least common dividend of 9, 11, 13, 
15, and 17? Ans. 109395. 
24. Find the least common dividend of 7, 14, 16, 21, 
and 24, Ans. 336. 
25. Find the least common dividend of 6, 11, 18, 33 
and 386. Ans. 396. 
26. Find the least common dividend of 2, 5. 7, 9, 11 
and 15. Ans. 6930. 


27. Find the least common dividend of 9, 18, 27, 36, 
45, and 54, Ans. 540, 


VULGAR FRACTIONS. 77 


28. Find the least common dividend of 2, 38, 5, 7, and 


ll. Ans, 2310. 
29. What is the least common dividend of 4, 5, 8, and 

92 Ans. 360. 
30. What is the least common dividend of 2, 3, 4, 8, 

1], and 16 2 Ans. 528. 
31. What is the least common dividend of 2, 5, 13, 

16, and 192 Ans. 19760. 
32. What is the least common dividend of 4, 10, 14, 

15, and 21 2 Ans, 420. 

FRACTIONS. 


Arr. 102, What is a Fraction ? 

A Fraction is one or more of the equal parts into which 
a whole number may be divided, 

Arr. 103. How many classes of Fractions are there ? 

Two ; Common ond Decimal Fractions. 

Art. 104. What is a Vulgar Fraction ? 

A Vulgar Fraction is one that is expressed by two num- 
bers written one above the other with u horizontal line be 
tween them. 

Art. 105. What is the upper number called ? 

The numerator. 


Art. 106. What is the lower number called ? 
The denominator. 


Arr. 107. What does the denominator express ? 

The denominator expresses into how many equal parts 
a unit is divided. 

Art. 108. What does the numerator express ? 

The numerator expresses how many of those equal parts 
are to be used, 


Norz.—The numerator av.d denominator taken together are called the terme 
of a fraction. ne 


78 VULGAR FRACTIONS. 


Arr. 109. How many kinds of Fractions are there ? 

Siz :—Proper, improper, mixed numbers, simple, com- 
pound, and complex. 

Art. 110. What is a Proper Fraction ? 

Lt is a fraction whose numerator is less than its denomt. 
nator. 
Art. 111. What is an Improper Fraction ? 


Lt is a fraction whose numerator is equal to, or greater 
than tts denominator. 


Art. 112. What is a Mixed Number ? 

It is composed of a whole number and a fraction. 

Art. 118. What is a Simple Fraction ? 

It is a fraction whose numerator and denominator are 
whole numbers. 

Arr. 114. What is a Compound Fraction ? 

It is a fraction of a fraction, or several simple fractions 

joined by the word “ of.” 
Arr. 115, What is a Complex Fraction ? 

lt is a fraction that has a fraction in the numerator or 
denominator, or in both. 


Art. 116. What alteration is made inthe value of afrac 
tion by dividing or multiplying both terms by the same 
number 2? 


No alteration. 


Art. 117. What is altered ? 
The form of the fraction only is altered, 


Art. 118. Why does the division or multiplication 
of both terms of a fraction by the same number make 
ao alteration in value ? 

Because the value of a fraction does not depend singly 
upon the numerator, or upon the denominator, but upon the 
relation that one holds to the other. 


VULGAR FRACTIONS, 79 


REDUCTION. 


119. T’o reduce a fraction to its lowest terms. 


Ruite.—Divide both terms by their greatest comiron 
divisor, or by their common factors. 


1, Reduce 24 to its lowest terms. Ans, 2. 
2. Reduce 33 to its lowest terms. Ans, 1. 
3. Reduce 14 to its lowest terms. Ans. 7%. 
4, Reduce 28 to its lowest terms. Ans. 75. 
5. Reduce 2% to its lowest terms. Ans. 2. 
6. Reduce 22 to its lowest terms. Ans. 2, 
7. Reduce 24 to its lowest terms. Ans. 2. 
8. Reduce ,°% to its lowest terms. Ans. 3. 
9. Reduce 134 to its lowest terms. Ans. 4. 
10. Reduce 13% to its lowest terms. Ans, 4. 
11. Reduce 22& to its lowest terms. Ans. é. 
12. Reduce ;37,% to its lowest terms. Ans. ~&. 
"3. Reduce 74'45 to its lowest terms. Ans. 352, 
.4. Reduce 212 to its lowest terms. Ans. 128. 
15. Reduce 3.959, to its lowest terms. Ans. 2J.. 
16. Reduce 32529 to its lowest terms. Ans. 3%. 
17. Reduce 4453? to its lowest terms. Ans. 33. 


Arr. 120. To reduce Improper Fractions to whole or 
mixed numbers, 


Rurz.-—Divide the numerator of the fraction by the 
denominator, and if there be a remainder place it above the 
divisor in the form of a fraction, and annex it reduced to 
tts lowest terms to the whole number in the quotient. 


18. Reduce 2,7 to a whole number. Ans. 3. 
19. Reduce 47 to a whole number. Ans, 13, 


20. Reduce +2%° to a mixed number. Ans. 873. 


80 VULGAR FRACTIONS, 


21. Reduce 250 | to a mixed number. Ans. 1633. 
22, Reduce ++ 300" = to a mixed number. Ans, 32}. 
23. Reduce = 


1 to a mixed number. 
9 
© toa mixed number, 
Ans. 4411, 


25, Reduce 437° to a mixed number. Ans. 20754- 
26. Reduce SS to a mixed number. Ans. 13833. 
27. Reduce 2212° to a whole number. Ans. 338. 


175 


ace brie 
28. Reduce —49- toa mixed number. Ans, 7824 


29. Reduce &3991 to a mixed number. 
Ans. 49 34. 


30. Reduce 4373" to a mixed number. Ans. 1063. 


31. Reduce 74853 to a mixed number. 

Ans, 17#8 
382. Reduce © aie o21 to a mixed number. 

Ans. 567i 


94, Reduee + 


Arr. 122. To reduce a whole or mixed number to an 
improper fraction, 


Rutz.—/f the number be whole, multiply it by the 
number required for a denominator and place the product 
over it ; 

If the number be mixed, multiply the whole number by 
the denominator of the fraction, to the product add the 
numerator, and place the sum over the denominator. 


Art. 123. What is the simplest form of reducing a 
whole number to the form of a fraction ? 
Place a unit under it. 


33. Reduce 171 to an improper fraction. Ans 35, 


34, Reduce 474 to an improper fraction. 
Ans. +>. 


50. 
De 
pe 46. 
52, 


. Reduce 18 to fifths. ANS. 5. 


. Reduce 95 to sevenths. Ans. a 
. Reduce 753 to an improper fraction. 


. Reduce 321 to fifteenths. Ans. 


lo 
. Reduce 171 to thirty-thirds. Ans, 2243, 
. Reduce 49614 to an improper fraction. 


REDUCTION, 81 


. Reduce 687 to an improper fraction. 


§51 
Ans. —. 


680 
iis, 


. Reduce 45}5 to an improper fraction. 


Ans, 552, 


Ang soe 


. Reduce 729,%, to an improper fraction. 


18229 
Ans. —33—. 


. Reduce 463312 to an improper fraction. 


8341 
Ans. = ‘ 


. Reduce 165445 to an improper fraction. 


496237 
Ans. mis00 


. Reduce 437514 to an improper fraction. 


Ans, 122832 
Tike ier, 


. Reduce 78003, to an improper fraction. 


299305 
Ansha iu: 


. Reduce 84574, to an improper fraction. 


122477 
ITEP Caappeen 


. Reduce 7547 to an improper fraction. 


Ans 6797 
° 9 0 ° 
Reduce 4800 to seventy fifths. Ans, =°92°°, 


Reduce 147 to a fraction whose denominator shall 


6762 
Ans. yee 


Reduce 6875 to a fraction whose denominator 


shall be 360. Ans, ae 


82 


VULGAR FRACTIONS. 


Art. 124, To reduce compound fractions to simple 
ones, 


Rutz.—/J/f the fractions that compose the compound 
fractions are simple, cancel all the factors common to nu- 
merators and denominators, and then multiply the remain- 
ing numerators together for a numerator, and the remain- 
ing denominators for a denominator. If the proposed 
Sraction contain mixed numbers, reduce them to improper 
Sractions, and proceed as before. 


53. Reduce + of } of {8 to a simple fraction. 
Ans. 45. 
54, Reduce 2 of 2 of $ to a simple fraction. 
3 Ans. 35. 
55. Reduce of 4 of 18 to a simple fraction. 
Ans. SET 
56. Reduce ¢ of $ of 3 of 38 to a simple fraction. 
Ans, 12, 
57. Reduce 1% of 2 of % of +4 of 12 toa simple frac. 
tion. Ans. 723. 
58. Reduce $ of 1 of # of {2 to a simple fraction. 
Ans. 5°,. 
59. Reduce 5°, of; 35 of 3 of ~; to a simple fraction. 
Ans. g}>. 
60. Reduce 2 of 31 of 250 to a simple fraction. 
Ans. 5834. 
61. Reduce 4 of 33 of 2} to a simple fraction. 
Ans, 63, 
62. Reduce ¢ of 3 of 22 of 6% to a simple fraction. 
112. 
63. Reduce 33 of 7; of 14 of 43 to a simple fraction, 
Ans. 1,4. 
7 se Reduce 75 of 63 of 32 of 3% of 73 toa ye 
action. ns. 773721, 
65. Reduce }4 of 161 of 774 of 183 to a simple frac- 
tion. Ans. 21653. 
66. Reduce 5 of 44 of 43 af 161 of 2 to a simple 


fraction. Ans. 453. 


REDUCTION. 83 


Art. 125. To reduce complex fractions to simple frac- 
tions, 


Ruitz.—Z/f the numerator and denominator be simple 
fractions, invert the denominator, place the numerator 
after it, with the word “ of” between, and proceed as in 
compound fractions; if there be mized numbers in the nu~ 
merator or denominator, reduce them to improper fractions, 
and proceed as before. 


2 
67. Reduce — to a simple fraction. Ans, 3 
3 
8 
68. Reduce — to the simplest form. Ans, 1%. 
16 
5. 
69. Reduce 1'5 to a simple fraction. Ans, §. 
16 
ale Y 
70, Reduce 22 to the simplest form. Ans. 1]. 
13 
33 
aie 
71. Reduce ey; to the simplest form. Ans. 124. 
1 
i 
72. Reduce 3a to simple fraction. Ans. #5. 
3 
73. Reduce + to a simple fraction. Ans. 24, 
8 
4 
74, Reduce —7 to a simple fractior Ans. 3). 
t 
75. Reduce 5. s to a simple fraction. Ans, +555. 
13 
i fle 
76. Reduce oF to a simple fraction. Ans. 3. 
ves 
13h , 
77. Reduce ar to a simple fraction. Ans. yy. 
3} ee - 
78. Reduce —~* to a simple fraction. Ans. y5 


63 


VULGAR FRACTIONS. 


2 
79. Reduce ae to a simple fraction. Ans. 2. 
873 7 
80. Reduce 00 *° 2 simple fraction. Ans, 4 
433 : 
81. Reduce TH to a simple fraction. Ans. 7%. 
933 ! , 
82. Reduce 759 to a simple fraction. Ans, +3 
68% 
83. Reduce jo to a simple fraction. Ans. 44. 
84. Reduce = to a simple fraction. Ans. §. 
2 
334 
85. Reduce G2 1° ® simple fraction. Ans, + 
3 
152 , 
86. Reduce 313 °° 8 simple fraction. Ans. $. 
4 
11 
87. Reduce i ae i to a simple fraction. Ans. ;. 
13 
72 
88. Reduce 1882 to a simple fraction. Ans. +4555. 
R 151} : : 9075 
89. Reduce iL: to asimple fraction. Ans. 9°75. 
15 
15 
90. Reduce 440 to a simple fraction, Ans. 129. 
91. Red a, imple fraction. Ans. -22.67 
. iveduce 11i2 to asimple traction. sins. 3"5°37;'5. 


Art. 126. To reduce compound fractions that contain 


complex fractions, to simple ones, 


Rutz.—Reduce the complex fractions to the simple ones, 


and proceed as in the reduction of compound fractions. 


REDUCTION. 85 


92. Reduce 3 of = of 2 E to a simple fraction. 


38 
Ans. 35% 


93. Reduce 24 of 193 of = a to the simplest form, 
Ans. 243. 


n 
94. Reduce of ix to a simple fraction. 
: Ans. 385° 
95. Reduce 12 of —% of 103 to the simplest form. 
3 


Ans. 1545. 


2 3 
96. Reduce = of “4 of 164 to a simple fraction. 
y Ans. 


on] 
[om 
es 


1 
97. Reduce = of — of 29 to the simplest form. 
3 
Ans, 74}. 


98. Reduce a4 of 5 — of 19 to the simplest form. 


50 = 
Ans. 11}. 


3 
Reduce 141 of 7 of i 


99 to the simplest form. 


Ans, 5,8. 
91 
) ae 
00. Reduce = 7 : aS i 133 of io +o a simple fraction, 
Ans. 338. 


101 Reduce of 53 of 994 to the simplest form. 


7 
Ans, 3755. 


86 VULGAR FRACTIONS. 


Art. 127. What is the Common Denominator of 
several fractions 2 


It is the common dividend or multiple of their de..omt- 
nators. 


Arr. 128. To find the least common denominator cf 
several fractions, 


Rutz.—Find the least common dividend or multiple of 
the denominators. (Art. 101.) 


Art. 129. To reduce fractions to their least common 
denominator, 


Ruite.—Reduce the improper, compound, and complex 
fractions to their simplest form; find the least common 
dividend of the denominators ; then divide the denominator 
of each fraction separately into the common denominator, 
multiply the quotient by the numerator, and place the pro- 
duct over the common denominator ; proceed in the same 
manner with each of the given fractions, and they will be 
reduced to others having a common denominator. 


102. Reduce 4, 2, $, 4 to their least common deno- 


. 42 16 2 
minator. Ans, 42, 18, 2 


~~ 


1 
+ 
103. Reduce 2, 2, #, and 74, to their least common 


; Lie eR 32 
denominator. Ans. 5, o's, woo, and FA. 


104. Reduce ;%, 4, 2,2 and 75, to their least commoz 
denominator. Ans. 4 


jJenominator. He. 


106. Reduce 72, ;4, and 1 $ to their least common 


denominator. Ans. 7482 


ADDITION. — 87 


107. Reduce 3%, 8;3;, and 433 to their least com- 
mon denominator. Ans. +4, 832, and 4233, 
108. Reduce 3 3 of 345, 7; of 34, and 172 to their least 
common denominator. Ans. 35, 1x5, 1742. 
109. Reduce 2 of $ of 104, 4 of 42 of 44 of 2,and 18 
to their least common denominator. Ans. 6, 124, oe 
110. Reduce 1, 3855 7, and 7; to their least com- 
mon denominator. Ans, 3283, 3 
111. Reduce 2 of 173, 3% of +4, 2 
_5 62575 


common denominator. Ans. 6 


112. Reduce $ of 23, 3% of 3, § of —, to their least 


common denominator. Ans, 1219, ,89,. ,€%,. 


62 
DUR ee eee 2 of oe eir 
113. Reduce 44, 508, 26, and $ of 9 te their leas6 


common denominator. Ans, 11,447 4 


6 
114. Reduce 12 of ;% of — ay 2, 74,64 to their least com- 


6 
inon denominator. i yess 95555, 7855, 6 55- 
115 Reduce }4, ;5 to fractions whose denominators 
2842) 
shall be 30. Ans, 28, 24. 
116. Reduce 4, , and 1 to fractions whose denomina- 
Ke 6 : 
tors shall be 70. Ans. $8, 9, and 2. 
Se. 457 ! 
117. Reduce 3%, #5, 1s, and 41 to fractions whose 


denominators shall be 300. Ans. =45,, #4, 449, 132. 


88 VULGAR FRACTIONS, 


ADDITION. 


Art. 130. To add simple fractions, 


-Ruitz.—Reduce the fractions to their least common 
denominator, add their numerators together and place the 
sum over the common denominator ; if the result be an 
improper fraction reduce it to a whole or mixed number. 


118. Add 4, 3, % #, and 7%. Ans, 24%, 
119. Add 4, 75, $ and 22. Ans. 2237, 
120. Add $, 7, 44 and 2. Ans, 24%. 
121. Add 3, 3%, 4, $ and 3. Ans, 2224. 
122. Add 7%, 4, $, 34 and 4. Ans 2,5. 


123. What is the sum of 4, ;%, 4, 2,, and}? 
124. What is the sum of 53;, 743, 25, } and 


125, What is the sum of 75, $5, 3, and 34? 


Ans, 2} 
126. Add 1 Too so) ay and 2, Ans, 15355 
127. Add 4, 13,28, 12 and 44. Ans, 3,82. 


Art. 131. To add mixed numbers, 


Ruiz.—Add the fractions, and to their sum add the 
sum of the whole numbers. 


128, Add 44, 63, 2} and 3. Ans, 1314, 
129. Add 108, 7%, 82 and 163. = Ans, 4248. 


ADDITION. 89 


130. Add 1,5, 62, 1838 and 235. Ans. 2843, 
131. What is the sum of 2,3,, 63 and 1243. 


Ans. 672,23 
1383. Add 23, 131, 998, 512.4. Ans, 627493. 
134. Add 14,6, 314 and 88,%. Ans. 106283. 


135. Add 90075, 450,35, and 696,%. 
Ans. 20473555. 


136. Add 1214, 98;% and 1424. Ans. 234745. 
Art. 132. To add compound and complex fractions, 


Ruite.—Leduce the compound and complex fractions to 
sumple ones, and add as before. 


» 37. Add 2 of 12,2 of 74, and $ of 25. 
Ans, 3612. 


138. Add ,& of 114, § of 75 of 64 and 14 of 13. 
Ans. 1932. 
139. What is the sum of $ of 14, $ of 86 and 1% of 


1010? Ans. 726275. 
140. What is the sum of % o 74 of 21, $ of 182 
and 773 2 Ans. 230325. 


141, Add 7% of $ of 20, $ of $ of 24} and {4 of 2} 
Ans. 21,45. 
142, Add 4; of 93 and x4 of 8693. 


ue Ans. 16773%. 


90 VULGAR FRACTIONS. 


143, Add =? 4 of 17, and $ of = Ans, 434. 
52 18% | 122 
Ee ly a raat : ; 
144. Adi 55 of 9, and 5, Ans. 133 
145, Add § of of 114, # of 5 and 7 
Ans, 744. 
98 Th 44 
146. What is the sum of —— 50, is, 304 and $ of 1742 
Ans, 1621, 


720° 


19} 81} 
147. What is the sum oad, Bik, and 54 of 24? 


445 
Ans. 1544 ye 


42 a 
2} 47 
148. What is eke sum yee 30, 9, and — of 30? 
one 1p: 
63 
149. What is the sum of | —t E of 142, at of 4 ane 
150. What is the sum of 662 of 3 85 and 2 of 3 of 
142, 154 
31 
19 of 50° Ans. 14775 


151. A farmer had 3 fields: the 1st. contained 312 
acres ; the 2d., 492 acres, and the 3d., 59,5 acres; how 
many acres had he in all ? Ans. 140192 acres, | 


SUBTRACTION, 91 


152. A man earned in one day $388, in the 2d., $44, in 
the 3d., 5,5, in the 4th., $74, in the 5th., $4,%, and in the 
6th., $82; how much did he earn during the week ? 

Ans. $288. 

153. There were 5 loads of hay weighed on the county 
scales ; the Ist. weighed 172 cwt.; the 2d., 192 cwt. ; the 
3d 182 cwt.; the 4th., 192 ewt.; and the 5th., 16,5; cwt. ; 
how much did the 5 loads weigh ? Ans, 9135. 

154. A grocer bought 7 firkins of butter, weighing 
respectively 554, 543, 552, 562, 537, 56 and 552 Ibs. ; 
how much did they weigh together? Ans. 387,°9, |b. 

155. If a person work on Monday 82 hours, on Tues- 
day, 92 hours, on Wednesday, 8,3; hours, on Thursday, 
10% hours, on Friday, 9$ hours, and on Saturday, 10} 
hours; how many hours will he have worked during the 
week ? Ans. 5732%5 hours. 

156. A person travelled in one day 172 miles ; in the 
second, # of what he went the first day; on the third, 
227 miles; and on the fourth 86} miles; how far did he 
travel in 4 days. Ans. 892 miles. 

157. A cartman carried in one load 162 ewt.; in a 
second, 172 cwt.; in a third, $ of the sum of the other 
two; how much did he carry in the three loads ? 

Ans. 503% cwt. 


SUBTRACTION. 


Art. 133. To subtract simple fractions, 


Ruitr.—Reduce the fractions to a common denominator, 
subtract the less numerator from the greater, and place the 
difference over the common denominator, 


158. Subtract 2 from 4. Ans, 4. 
159. Subtract ¢ from 7. Ans, 43. 
160. Subtract 14 from 32. Ans. 3b. 
161. Subtract 4 from 32. Ans. zg. 


92 


162. 
163. 
164, 
165, 


Art, 


Rutz.— Place the less mixed number under the greater, 
with the whole numbers and fractions under each other ; 
subtract the fractions first, and afterwards the whole num- 
bers ; if the under fractions be greater than the upper add a 
unit to the upper fraction, and subtract the under one from 
their sum, set down the difference and carry “oNE” to the 
units of the subtrahend, and proceed as in simple sub 


straction. 

166. From 25% take 153. - Ans. 1075. 
167. From 1953 take 118}. Ans, 777%. 
168. From 753 take 122. ' Ans. 634. 
169. From 1662 take 111{. Ans. 553. 
170. From 11494 take 249,%. Ans. 90023. 
171. Subtract 796, from 1344,4. Ans. 548,5. 
172. Subtract 452 from 984. Ans, 528, 
173. Subtract 65, from 150,4. Ans. 8412, 
174. Subtract 700% from 100055. Ans, 2994. 
175. Subtract 499,77, from 10994. Ans. 5992 
176. Subtract 386711 from 4019,%. 

Ans. 151398, 
177. Subtract 6914, from 10085. 

Ans. 316533,5. 
178. Subtract 386,99, from 1440-885. 


VULGAR FRACTIONS. 


From ,§ take ,%. Ans. 375- 
From 1% take =%. Ans. 27, 
From 23 take 14, ADS, saat: 
From 12 take 31. Ans, 223. 


134. To subtract mixed numbers, 


Ans. 1053,5%5. 


SUBTRACTION. 93 


Art. 135. To subtract compound and complex frac- 
tions, 


Ruiz.—Reduce them to simple fractions, and subtract 
as before. 


179. From } of $ take 2 of yh. Ans. 7435- 
180. From } of 32 take 4, of 24. Ans. 4. 
181. From 2 of 73 take 4 of 24, Ans. 1445. 
182. From % of 6% take 2 of 4 of 114. 
Ans, 455 
6 24 
183. From 50 take 7p, Ans, 34. 
4 1 
184, From Ti take oa Ans. 33, 
Tenetrone * teke © Atami 
° rom 12 take 7. us, 9387 
186. From $ of 2 of 34 take 7% of 4%. 
Ans, 237 
2 
187. From , of 63 take 4 of am Ans. 4585. 
94 84 
188, From 351 take 3B. Ans. 545. 
189. A man had $100, out of which he spent $433; 
how much had he left? __ Ans. $564. 
190. John has $4,;%.; William $313; how much more 
has John than William ? Ans. $4 or 50 cts. 


191. A person having $492, went to Boston, to which 
place the fare was $42; he afterwards went from Boston 
to Portland, and that cost $575; how much had he left 
when he arrived at Portland ? Ans. $39.30. 


94 VULGAR FRACTIONS. 


192. A man bought a firkin of butter weighing 56,3 
Ib. ; he sold 4 of it to one person, and 132 Ib. to another : 
how much had he left ? Ans. 14549; lbs. 


193. A merchant bought 2 pieces of cloth; the first 
piece was 38% yd. long, and the second, 414 yd. He 
sold 594 yd; how many yards had he left ? 

Ans, 2022 yd. 


194, A grocer bought 2 hhd. of sugar, each weighing 
1302 Ib; he sold 4 “of one hhd., and 455 2. Ib. of the 
other ; how much had he left out of both ee 2 

Ans. 1714, Ib. 


195. A jeweller had 3 parcels of gold; the Ist weigh- 
ed 1 lb. 54 oz., the 2d., 12% 0z., and the 3d., 3 lb. 84 oz. 
He manufactured # of the whole into spoons, and sold 1 
lb. of it; how many ounces had he left ? 

Ans. 611 oz. 


196. A wine merchant bought 2 pipes of wine; the 
Ist gauged 1163 gal.; the 2d., 119,35. .To one person 
he sold 39 gal., ‘to another 454 gal., and tu a third, 1004 
gal; how many gallons had he left 2 Ans. 50% g gal. 


197. From % of 34 take j of 7/5 of 74. 
198. Subtract 2 of 1,2, from $ of 12 of 5. 
Ans, 139 
° 456° 
3 
199. Subtract 14 of $ of 14 from $ of 2 of - 
Ans, $981. 


200. A merchant bought 2 lots of corn; the first 
measured 1000 bushels, and the second, 12982 bushels ; 
he sold 4 of the first lot and 1 of the second; how much 
more did he sell out of the first lot than out of the 
second ? Ans. 993%5 bu. 


201. A person bought a house for $3450, and sold it 
for $83314; he bought another house for $65024, and 


MULTIPLICATION, - 95 


sold it for $7000; did he gain or lose by the two trans- 
actions, and how much? Ans, $3782 gain. 


202. A person at his death left by his will $100000 
to be distributed as follows ; $50000 to his wife, 241874 
to his son, 12090,4 to his daughter, and the remainder 
to a charitable institution ; how much did the institution 
receive ? Ans. $138722,>. 


203. A company proposed to raise $1000000; the 
expenses attending were estimated at $28122; A sub- 
scribed $150000, B 459113, C $4963242, and D the 
balance ; how much must he subscribe in order to raise 
the capital, and pay the expenses ? 


Ans, $310576223. 


MULTIPLICATION. 


Art. 136. To multiply a fraction and whole number 
together, 


Ruiz.—Multiply the numerator of the fraction by the 
whole number, and place the product over the denominator ; 
or, cancel the factors that arecommon to the denomina- 
tor and whole number, and multiply as before. 


Notrt.—The word “or,” used in compound fractions, is equivalent to the 
sign x. 


204. Multiply 4 by 8. Ans, 44. 
205. Multiply & by 16. Ans. 8§. 
206. Multiply 138 by 3%. Ans. 7;};- 
207. Multiply 15 by 5%. Ans. 184. 
208. Multiply 28 by 27. Ans, 222. 
209. Multiply 24 by 18. Ans. 153%. 


210. What is the product of 39 and 48? 
Ans, 3218, 


96 VULGAR FRACTIONS. 


211. What is the product of 22 by 85% 
: Ans. 82}. 

212. What is the product of $3 by 44? 

Ans, 393. 


Art. 137. To multiply a mixed number by a whole 
number, 


Rure.—Multiply the fraction of the mixed number by 
the whole number, and to the product add the product of 
the two whole numbers. 


213. Multiply 7f by 8. Ans, 63. 
214, Multiply 8,5 by 15. Ans. 1803. 
215. Multiply 47 by 33. Ans. 1764. 
216. Multiply 19 by 62. Ans. 1293. 
217. Multiply 4534 by 5. Ans. 229355. 
218. Multiply 754%, by 68. Ans. 475194. 
219. Multiply 208 by 17,§. Ans. 3590.5. 
220. Multiply 8000 by 7£. Ans. 23625, 
221. Multiply 407.4 by 188. Ans, 7655913. 


Art. 138. To multiply two or more fractions to- 
gether, 


' Rupz.—Cancel the factors common to the numerators 
and denominators, and then multiply the remaining 
numerators together for the numerator of the product, and 
the remaining denominators together for the denominator 
of the product. 

If there be mixed numbers reduce them to improper 
Fractions. 

If there be compound or complex fractions reduce them 
to simple fractions. 


222. Multiply 2 by 3. Ans, 34 
223. Multiply ;4 by 14. Ans. 35°. 


MULTIPLICATION. 

224. Multiply +6 r by $. Ans. 12, 
225. Multiply §, 7 and 3 together.. Ans. 4. 
226. Multiply 83 by &. Ans. 713. 
227. Multiply +2 by 122, Ans. 114. 
228. Multiply 74 by 183. Ans. 1402. 
229. Multiply 3732 by 613. Ans. 233121, 
230. Multiply 2 of 17 by 23. Ans. 934, 
231. Multiply 132 by 4 of 82. Ans. 554. 
232. Multiply 662 by § of 16,5. Ans. 9853. 
233. Multiply 54 of 2 by 43 of 16. Ans. 

234, Multiply 3 off ‘of 7 Ree 4 of 99. Ans. 744. 


236. 


201 2 


239. 


2A0. 


241. 


242. 


. What is the product of 196 by 
* Ans, 1103. 


. Multiply 4 of 8125 by 2 of 8000. 
Ans. 7142853. 


What is the product of ~ of $ of 14% by 43 
faa 1295-4335. 


. What is the product of = 3 bY 18? Ans, 44 


yeus 
are) 
14 


What is the product of 7 by 6100? 


Ans, 38888. 


vee 
What is the product of 5 a a by 43% 


gl 

Multiply vo by a Ans. ie 

Arbre by oe Vee 
u tiply 50 by 202" Ths. 6? 


97 


98 VULGAR FRACTIONS. 


, 124 
243. Multiply 6 by 7 Ans. 513. 
244, Multiply or by pata Ans. £29 
Y oe 182 12, 2277 
‘ 32 12 991 
245, What is the product of 3, isi an 10032” 
Ans, $2298, 


: 955 
246. What is the product of isi by 75 of 18 of 534 


7 
Ans. 1,4. 


i 
247. What is the product of 24 of = and 2 of %, of 
: ’ 
$! y) A 873 
is of 100? ns. 955%. 


When th? 4»'ve of a single article is given, how can the value of 
any number 2f articles be found? (Art. 34.) 

When the quantity that can be obtained for one dollar, one shil- 
ling, &e., is given, how can the corresponding quantity for any num- 
ber of dvllars, shillings, d&e., be found ? 

2445. What will 94 yard? of muslin cost at % of a 
dollar per yard ?, Ans. $562. 

249. What will ;5 cf @ bushel cost at '75 cts. a bushel ? 

Ans. 432 cents. 


350. What will 171 acres cost at 13 dollars an acre? 
Ans. $1603%. 


251. What will 186 gallons cost at £41 a gallon ? 
Ans, £12111, 


252. What will .4. of a pound cost a 15 cts. a pound ? 
Ans. 22 cents. 


253. If 251 yards of cloth can be exchanged for one 
aere; how many yards can be obtained for +2 of an 
acre ? Ans. 23775 yards. 


MULTIPLICATION. 99 


254. What is the price 17 loads of wood at $2? per 


load ? Ans. $463. 
255. What will 103 yd. of cloth cost at ie per yd. 
Ans. $734. 

256. If one hhd. of molasses cost $1774, what will 
100 hhd. cost ? 2 Ans, $1763,5. 

257. If a man can earn $332 in one week, how much 
can he earn in 52 weeks ? Ans. $17332. 

258. What must be paid for 600 barrels of flour at 
$52 per barrel ? Ans. $3225. 


259. What will be the cost of a square mile of land at 
$1312 per acre ? Ans. $841958. 


260. If it take 1050975 ft. of boards to build a house, 
how many feet will be required to build 7 houses ? 
Ans. 735674, ft. 


261. A merchant bought 100 barrels of flour for $6 
per barrel ; he sold 49 barrels at $74 per barrel, and the 
rest at $72 a barrel ; how much did he gain ? 

Ans. $4383. . 


262. A farmer bought 43 acres of land at $104¢ an 
acre ; 16 cows at S988 each ; 2 ploughs at $115 each ; : 
what was the total amount? Ans. $4985. 


263. What cost 332 Ib. of tea at 933 cts. per Ib. ? 
Ans. $31.25, 


264. What will 452 gallons cost at $214 per gallcn? 
Aes $1325. . 


265. What will 1804 acres cost at $255,%, per acre? 
Ans. $461834h 


_ 266. A person bought 1800 bushels of corn for 143 
cts. per bushel ; 16604 bushels of wheat at 874 cts. per 
bushel, and 3802 bushels of rye, at 58 cts. per bushel ; 
what was the value of the whole? Ans. $2458.63,5. 


100 VULGAR FRACTIONS. 


267. A man bought a farm containing 3192 acres, at 
$200 per acre; he sold 2504 acres at $250 per acre; 
and the remainder at $2662 per acre; how much did he 
gain ? Ans, $17111421. 


268. A had £7888, B had £60038, A tripled his 
money, and B quadrupled his; how much did they then 
have together ? Ans. £4768¢4. 


ee 


DIvisp Tow, 


Art. 139, To divide a fraction by a whole number, 


Ruiz.— Divide the numerator of the fraction if possible 
by the whole number, and place the quotient over the 
denominator; or, multiply the denominator of the fraction 
by the whole number, and place the product under the 
numerator. 


Art. 140. To divide a whole number by a fraction, 


Rote.—ZJnvert the fraction and multiply it by the whole 
number. 


269. Divide 24 by 7. Ans. 75. 
270. Divide $& by 4. Ans. 4. 
271. Divide 7 by 5. Ans. 75. 
272. Divide 12 by 6. Ans. 33. 
273. Divide 28 by 4. Ans. 35. 
274. Divide 12 by 12. Ans. 345. 
275. Divide 15-by 3, Ans. 20. 
276. Divide 27 by 4%. Ans. 30. 
277. Divide 48 by 24. Ans, 52,4. 
278. Divide 100 by 42. Ans. 130. 


279. Divide 500 by 3 Ans, 13834. 


DIVISION. 101 


280. Divide +47 by 28. Ans. 24. 

281. Divide 903 by 54. Ans. ,§7>- 
282. Divide 750 by 1%. Ans. 11024. 
283. Divide 1000 by $. Ans. 11662. 
284, Divide 1499 by 32. Ans, 241728 


Arr. 141. To divide a mixed number by a whole 
number, 


Rutz. Jf the dividend be less than the divisor, write 
the divisor under the dividend in the form of a complex 
fraction, and reduce to a simple fraction ; if the dividend 
_ be greater than the divisor, divide as in simple division, 
and place the remainder over the divisor, which will also 
form a complex fraction to be reduced. 


Art. 142. To divide a whole number by a mixed 
number, 


Ruiz.—Reduce the mixed number to an improper frac 
tion, invert it and multiply it by the whole number. 


Arr. 143. To divide fractions generally, 


Rute.—Invert the divisor, reduced if necessary, and 
multiply it by the dividend, also reduced ; observe the 
rules for multiplication of fractions, and cancel if possible. 


285. Divide 33 by 5. Ans. 3. 
286. Divide 14% by 27. Ans, 342. 
287. Divide 4592 by 600. Ans, 1378, 
288. Divide 48 by 33. Ans. 142, 
289. Divide 75 by 14,3. Ans. 54335. 
290. Divide 1144 by 6. Ans. 19545 
291. Divide 2592 by 12. Ans. 2143. 
292. Divide 34792 by 18. Ans. 193445 


293. Divide 16008; DY, 39 Ans, 410232. 


102 


294. 
295. 
296. 
297, 
298. 
299. 
300, 
301. 
302. 
303. 
304. 
305. 
306. 
307. 
308. 
309. 
310. 
dll. 
312. 
313. 


014. 


315. 


316. 
317. 
318. 
319. 


VULGAR FRACTIONS. 


Divide 10000 by 22%. 
Divide 148967 by 5955. 
Divide 80082 by 11. 
Divide 14301612 by 25. 
Divide 2 by 3}. 
Divide 74 by 102. 
Divide 13 by 4% 
Divide 1$ by 172. 
Divide 286,35 by 37. 
Divide 300.4 Py 63. 
Divide 4% by 23. 

Divide 455 by 32. 
Divide 61155 by 2074 
Divide 10000 by 163. 
Divide 10037 by 1662. 
Divide 1111 by 334. 
Divide #94 by 572. 
Divide 2 of 12 by 53 of 4 
Divide 4 of 33 by 19 of 74, 


Divide 3 of 7}, of 63 by 2 of 193. 


ee 7 
Divide 55, of 4 by Tai. 
Divide 53 Hopes i0F 
What part of 164 is 842 
What part of 3f is 14? 
What part of 1914 is 1594. 


How many times does 18)12 contain 1613 


1 
<— by 15 of = 


Ans. 48934 
Ans. O508.254. 
Ans. 273289, 
Ans. 572083. 
Ans. 4. 


Ans, 378 


23 
Ans. 1202 


chs & 
ol 69 


Pel 
3 
Mm 
aN 
“¢ 
fo 


(ac ml to] 
Ww WO ehm oy 
° . ° 


re 


re eat 
e e 


Ans. 610-2 


2 
4 
At 
27 
I 


Ans, 2 


e 
Colt * 
oe md dole 
° ° e 


Ans. 


1s" 
Uo... 
161 


Ans. 85 


DIVISION. 103 
320. Divide $+92 by ci ‘ Ans. 1.335 
321, Divide 153-1113 by aust) Ans. 475. 


When the value of a single article and the value of several 
are known, how can the number of articles be found? (Act. 54.) 


When the number of articles and their value are known, how 
ean the value of a single article be found? (Art. 53.) 


Notre.—The divisor and dividend must be of the same denomination except 
when the value of a single article is found. 


322. If 1 pound of sugar cost $,°,, how many pounds 
can be bought for $100 ? Ans, 320 Ib. 


323. If 17 pounds of rice cost $3, what will one pound 
cost ? Ans. $,% or 3;% cents. 


324, If 25 pounds of coffee cost $42, os will one 
pound cost ? Ans. $3). or 343; cents. 


325. If 13 yd. of muslin cost .%, what wil one yard 
cost ? Ans. 2 a 


326. If 2 bu. cost $1, how much will 30 bushels cost ? 
Ans. $80. 


327. If gal. cost $1, what will 300 gallons cost ? 
Ans. $540, 


328. If § of a ton cost $13, what will one ton cost? 
Ans, $14.853. 


329. If 12 bbl. cost $100, what will one barrel cost ? 
Ans. $115.38,%. 


330. If 4, ewt. of coffee cost £1, how much will 340 


ewt. cost ? Ans. £23334. 
331. If 39, lb. of sugar cost 292 shillings, what will 
1 pound cost v ‘Ans. 3g. 


332. If 368% yd. of cloth cost $18433, what will 1 yd. 
cost ? Ans, $5. 


104 VULGAR FRACTIONS. 


333. If 287; bushels cost $100, what will one bushel 
cost 2 Ans. $3212, 


427° 
334. If coffee is 13£ cts. per pound, how many pounds 
can you buy for $10? Ans. 72,2; lb 


335. How many bushels of wheat can be bought for 
£24 15s. at 74 shillings per bushel ? Ans. 66 bu. 


336. If a pound of tea cost 53s., how mow many 
pounds may be bought for £13 17s.% Ans, 512% lh. 


3907. If 8 yd. cost $2.78, what will 1 yd. cost ? 
Ans. $7.414. 


338. If 42% of an acre cost $7112, what is the price of 


an acre ? Ans. $9883. 
339. If 43 hhd. cost $103.274, what will one hogshead 
cost ? Ans. $158.88,%. 


340. How many pounds of coffee can be bought for 
$783, at =%; of a dollar per pound? Ans. 41947 Ib. 


341. How many gallons of wine can be pone for 


£371, at LY per gallon ? Ans. 7034 gal. 
342. If you can buy 9; of a yard for one dollar, how 
many dollars will buy 14382 yd. Ans. $37403. 


343. If you can purchase 54 yards of muslin for $1, 
how many dollars will 1000 yards cost ? 
Ans. $19042 


PROMISCUOUS EXAMPLES. 


2 ; 
Notr.—Indicate the following sums thus, 73 price of one bushel x2=prioe 


of 2 bushels. This illustrates one of the uses of complex fractions. 
344, If 374 oz. of silver cost $3814, what will 150 oz. 
cost ? Ans. $125. 


345, What will 85¢ A. cost at $1454 for 10 acres ? 
Ans, $52529%., 


PROMISCUOUS EXAMPLES. 105 


346. A person had £30003; he divided-it int > 7 equal 
pare and gave 44 of the parts to a benevolent society ; 
ow much did the society receive? Ans. £192883 


347. If 32 bushels of wheat cost $22, what will 2 


bushels cost ? ? Ans, $1.26. 
348. If'794 quarts of black-berries cost $18, what will 
103 quarts cost ? Ans. $2.40. 
349. What will 64 Ib. of tea cost at $31 for 164 
pounds ? Ans, $1.25. 
350. If 62 acres of land cost $4000, what will °3 
acres cost ? Ans. $3613 


351. Ifa man travels 4014 miles in 134 days, a far 
can he travel in one week, omitting Sunday ? 
Ans, 18143 mile. 


352. If a hogshead of brandy cost $189.3814, how 
much will 22 gallons cost ? Ans. $66.11. 


353. If 173 gallons of molasses cost $42, what will be 
the price of a hogshead and a half? Ans, $233. 


354. If 14§ cords of wood cost £39 15s., what will 23 
cords cost. Ans, 143, shillings. 


355. If A can mow an acre of ground in 3 days, and 
B in 2 days, how long would it take them both? 
Ans. 11 days. 


356. If A can perform a piece of work in 25 days, and 
B in 28 days, in what time could they both do ne 
Ans. 183} days. 


357. A can build a certain wall in 10 days, Bin 12 
days, and C in 15 days; suppose the three work toge- 


ther, and find how long it would take them. 
Ans, 4 days. 


106 VULGAR FRACTIONS. 


REDUCTION OF DENOMINATE NUMBERS. 


Art. 144. To reduce denominate fractions from a 
higher to a lower denomination, 


Rutze.—Multiply the given fraction by as many of the 
denomination next lower as will make a unit of the given 
denomination ; multiply this result as before, and so pro- 

. ? . tas z . . 
ceed tell the fraction is reduced to the denomination re- 
guired, 

Norr.—If the first product be an improper fraction, it may be reduced to a 
mixed number; then the whole number may be set aside and the fractional 
part reduced as in the rule ; and if this product be an improper fraction, pro- 
ceed in like manner; a collection of the whole numbers in the order of their 


denominations having the last fraction annexed to the lowest denomination 
will be the answer. 


358. Reduce £1 to shillings. Ans. 4s. 


359. Reduce £4 to shillings and pence. Ans. 6s. 8d. 
360. Reduce £7’; to shillings and pence. 
Ans. 8s. 4d. 


361. What is the value of £;% ? Ans. 10s. 8d. 
362. What is the value of £,%? Ans. 5s. 74d. 


363. Reduce 3; lb. Troy to its value in lower denomi- 
nations ? Ans. 18 dwt. 


364, Reduce = of a ton to ewt., quarters, &e. 
; Ans. 3 ewt. 0 qr. 125 Ib. 


365. What is the value in lower denominations of 4; 
of a mile? Ans, 2. fur. 86 rd. 2 yd. 


366. Reduce 34, hhd. to gallons, &c. 
Ans. 2. gal. 0 pt. 31 gi. 


367. What is the value of 7 of a mile ? 
Ans. 6 fur. 8rd. 4 yd. 2 ft. 8 in. 


368. What is the value of 55 of 2 days? 
Ans. 13 hr, 26 min. 24 see, 


369. Reduce 3 of an acre to its proper value in lowe 
denominations, Ans. 2 R. 34 sq. rd. 8,9, sq. yd. 


REDUCTION OF DENOMINATE NUMBERS, 107 


. Reduce 334 lb. to dwt. Ans. 8112 dwt. 
. Reduce 14? tons to cwt. and Ib. 


Ans, 2853 cwt. 285713 Ib. 


. Reduce £274 to pence. Ans. 6560d, 
3. Reduce 314 bushels to quarts. Ans. 9982 qt 
. Reduce 122 miles to yards. Ans 218742 yd. 
. Reduce 127° E.E. to inches. Ans. 575 in, 
. Reduce 13923 degrees to miles. 


Ans. 970842 m. 


. Reduce 5954 miles to feet. Ans, 314880 ft. 
. Reduce 4593 acres to square rods. 


Ans, 735084 sq. rd. 


. Reduce 7112 hhd. to quarts. Ans. 1792724. 
. Reduce 123 years to days, 3654 days to the 


Ans. 4611.3, days. 


. Reduce 492 lb. to scruples. Ans. 14176 BD. 
. Reduce £18 72s. to pence. Ans. 44083. 
. Reduce £918 5s. 7% to pence. | 


Ans. 2203873d. 


. Reduce 11 oz. 173 dwt. to grains, 


Ans. 57014 gr. 


). Reduce 27 tons 18 cwt. 14 qr. to lb. 


Ans, 553428 Ib. 


. Reduce 13lb. 575 3 to grains. 


Ans, 7'7585-*. or. 


Ue x=) 


. Reduce 3 yd. 23 qr. to inches. Ans, 13132 in. 
. Reduce 13 m. 5,2, fur. to yards. 


Ans. 2404442 yd, 


. Reduce 39 deg. 41445 m. to yards. 


Ans. 4843760 yd, 


. Reduce 35 sq. m. 5002 A. to sq. poles. 


Ans. 3664060 sq. p. 


1s mt VULGAR FRACTIONS. 


391. Reduce 1395 7% cords to dude feet. 
Ans. 178616 cu. ft. 


392. Reduce 49,9, cu. yd. to cubic inches. 
Ans, 23281342 cu. in. 


' 893. Reduce 49 yr. 843 days to hours, 3654 days to 
the year. Ans. 450368 days. 


Art. 145. To reduce a denomifate fraction from a 
lower to a higher denomination, 


Rurz.—Divide the given fraction by as many of 
its own denomination as will make a unit of the denomi- 
nation next higher ; divide this result as before, and so 
proceed until the fraction is reduced to the denomination 
required, 


394, Reduce 1 oz. Troy weight to the fraction of 


pound. Ans. 75 Ib. 
395. Reduce 7 dwt. to the fraction of a poe 

Ans. 5339: 

396. Reduce 4 Ib. to ewt. _ Ans. zd ewt. 


397. Reduce 43 3 to the fraction of a pound. 
Ans. 5% |b. 


398. Reduce 53 oz. to the fraction of a cwt. 
Ans. xzh55 Cw. 
399, Reduce +2 qr. to the fraction of a yard. 
Ans. 4 
400. Reduce 24 in. to the fraction of a yard. 
Ans, 2; yd. 
401. Reduce 23 fur. to the fraction of a mile. 
Ans. 3° Mm. 


402. Reduce >> sq. p. to the fraction of an on 
Ans. zap A. 


403. Reduce 35 gal. to the fraction of a hhd. 
Ans. 335 hhd. 


REDUCTION OF DENOMINATE NUMBERS. 109 


404, Reduce 4 § gt to the fraction of a bushel. 
Ans. zh, bu. 


405. Reduce 42 hr. to the fraction of a week. 
Ans. 34$q wk. 


406. Reduce 14014 dwt. to pounds. 
Ans, 5493 Ib. 


480 
407. Reduce 64 Ib. to fraction of a cwt. 
Ans. ;}; ewt. 


408. Reduce 52d. to fraction of a pound. 
Ans. £545. 


409, Reduce 6112 gr. Apothecaries’ weight to drams, 
Ans. 10353. 
419, Reduce 112 in. to the fraction of a bi bi 
Ans. 35 yd. 


411. Reduce 10002 in. to ells English. 
Ans, 2217 E.E. 


412. Reduce 152 feet to the fraction of a rod. 
Ans, 23 rd. 


413. Reduce 28542 yd. to furlongs. 
Ans. 12139) fur. 


414, Reduce 75,5 sq. ft. to the fraction of an aCe, 
Ans, ya2559 A- 


Art. 146, To reduce a denominate number containing 
several denominations to the fraction of a particular 
denomination, 


Ruie.—Place the given number in the numerator and 
the one with whick itis to be compared, in the denominator ; 
reduce both terms to the same denomination, and then 
reduce them to their simplest terms. Or, 

Reduce the lowest denomination to the fraction of the 
next higher, and prefix the next higher denomination ; 
reduce this result as before until the whole is reduced to the 
denomination required, 

10 


110 VULGAR FRACTIONS. 


415. Reduce 3s. 4d. to the fraction of a £. 


Ans, } £. 
416. Reduce 6s. 8d. to the fraction ofa £. . 

Ans. 4 £. 
417. Reduce 13s. 4d. to the fraction of a £. 

Ans, 2 £. 


418. Reduce 5s. 64d. to the fraction ofa £. 
Ans. £57555. 


419. Reduce 6s. 53d. to the fraction of a £. 
Ans, 297, 
420. Reduce £5 16s. 104d. to the fraction of a £ 
Ans. £524. 
421. Reduce 3 oz. 11 dwt. 15 gr. to the fraction of 4 


pound. Ans, 234 Ib. 
422, Reduce 4 cwt. 3 qr. 18 lb. to the fraction of a 
ton. Ans. 493% T. 
423. Reduce 33 553 24059 to the fraction of a pound. 
Ans, }72 lb. 


424, Reduce HP: yd. to the fraction of a mile. 
Ans, $327 m. 


425. Reduce 7 sq. p. 11 sq. yd. 84 sq. ft. to we frac- 


tion of an acre. Ans. 7$}5 A. 
426. Reduce 2 qr. 3 na. 14 in. to the fraction of a yaid. 
Ans, 313 yd, 
427. Reduce 15 hr. 10m. 30 sec. to the fraction of a 
day. Ans, $87 day. 
428. Reduce 25527 days to the fraction of a ee of 
3654 days. Ans. 45 
429. Reduce % of § of 2 bu 3 pk. to ae i action of 3 
bushels. Ans. 745 of 3 bu. 


430. Reduce 13 ewt. 3 qr. 15 Ib. to the fraction of a 
ton Ans. 439 T, 


ADDITION OF DENOMINATE NUMBERS. 11] 


431. Reduce 8° 15’ 182” to the fraction of a circle. 
Ans. 7323, of a circle. 


432. Reduce 3{ in. to the fraction of a er 
Ans, 14 of a hand. 


433. Reduce 55} yards to metres. 
Ans. 51 metres, 


434, Reduce 214 yards to metres. Ans. 1911 m 


435. Reduce 84 metres to the fraction of 124 yards, 
Ans. $42 of 124 yd. 


436. Reduce 21 yards to aunes. Ans. 1# aunes, 


437. Reduce 452 yards to the fraction of 55 aunes. 
Ans. 7°37, of 55 aunes. 


- 488. Reduce 2 m. 6 fur. 39 p. 5 yd. 2 ft. 11 in. 2 b.c. 
to the fraction of a league. Ans, 278333, 


ADDITION OF DENOMINATE NUMBERS, 
Art. 147. To add denominate fractions, 


Rutze.—Reduce the fractions to their value in one or 
several denominations, and then add as wm addition of 
Jractions and denominate numbers. 


439, Add £2, £2 and 4s. Ans. £1 8s. 6d. 


440. Add £4, £2 of 3, 4s. and 3d. 
Ans, £1 4s, 0122d. 


441. Add 4 lb., 42 oz. and 314 dwt. 


Ans. 1 Ib. 4 oz. 
442, Add 144 lb. 183 oz. 2 oz. and 13% dr., Avoirdu- 
pois weight. Ans. 15 Ib. 11 oz. 13,83 dr. 


443, Add 2,3; tons, 172 ewt. and 22 qr. 
Ans. 3 T. 3 cwt. 2 qr. 1613 lb. 

444, Add 75% lb. 53 lb. 623 and 413. 
Ans. 13 bb. 635325 1143 gr. 


112 VULGAR FRACTIONS, 


445, What is the sum of 24 bu. 8} pk., 59 bu. 1 pk. 
1} qt., and 133 bushels? Ans. 97 bu. “L pk. 7 qt. 1 pt. 


446. Add 2 yd., 2 of 3 qr., and 3} na. 
Ans. 1 yd. 2 na. 14 in. 


447 Add 2 of 33 m., 54 fur., and 173 p. 
ANS. Van ot Si 13 ral 3 yd. 2 ft. 43 in. 


448, Add 4} deg., 69} m., 574; rods, and 4# yd, 
‘Ans. 5 deg. 9 m. ‘bie 14 p. 03 yd. 


449, Add 575 A., # of 64 A., a of a rood, and 4°; 
of 2,4, sq. p. Ans, 9 A. 3 R. 30 sq. p. 18 sq. yd. 

450. Add 53, of a cord, cu. ft., and 2 of 4 of 714 
cu. ft. Ans. 25 cu. ft. '7554 cu. in. 

451. What is the sum of 35 of 23 hhd., 4 of 22 gal., 
and 4 of 54 qt.? Ans. 2 hhd, 0 gal. 1 qt. 1,4 pt. 


452. What is the sum of 2 —— 2 of a bushel, 163 pk., 
and 2 of 3% of 34 qt. ? re 5 bu. 0 pk. 334 qt. 


453. sai is the sum of 3 of 865} days, 2 of 53 
bbs and 49+ minutes ? 
Ans. 33 wk. 1 da. 2 hr. 494 min. 


454. What is the sum of 4%5 of a circle, 32 signs, 2 
of a degree, and 2 of 54 minutes ! 
Ans. 5 signs 16° 16’ past : 


455. What is the sum of 5 T. 194 cwt. 34 q 
ewt., 6 T. 33 qr. 183 Ib., 44 T. 163 cwt., ae 15 aN 
16 cwt. 1 ar. 2+ lb. ? 

Ans. 33 T. 5 cwt. 2 qr. 53355 |b. 


LS) 


SUBTRACTION OF DENOMINATE NUMBERS, 113 


SUBTRACTION OF DENOMINATE NUMBERS. 


Art. 149, To subtract denominate fractions, 


Rute.——Reduce the fractions to their value in various 
denominations, and then subtract as in subtraction of frac- 
tions and denominate numbers. 


456. From £2, take 8s. 6d. Ans. 9s. 10d. 
457. From $32, take 50 cts. Ans. 162 cts. 


458. From $ ofa ton, take 33 ewt. 
; Ans. 16 cwt. 3 qr. 12, lb. 


459, From “to take 2s. 6d. rei 0. 
460. From 14 sq. m., take 2524 A. 

Ans, 274 A, 2 RB: 18545 sq. p. 
461. From 24°, take 2 of 1°. Ans, 85’ 253", 


4B 
462. From +5 of a league, take 4 of a m. 


Ans. 4 fur. Ord. 22 yd. 
463. From 8 bu., take 4 of 22 pk. 
Ans. 1 pk. 233 qt. 


464. From 2 of 182 |b., take 53 245. 
Ans. 11 1b. 113 53 25 14 gr, 


465. Subtract £17 10s. 82. from £91 6s. 64d. 
Ans. £78 15s. 102d. 
466. Take 13 tons, 3 ewt. 3 qr. 142 1b. from 19 tons 
l ewt. 8 qr. 17} 1b. Ans. 5 T. 18 ewt. 0 qr. 32; Ib. 
467. From 18 m. 1 fur. 13 rd. 31 yd. take 7 fur. 11 
rd. 42 yd. Ans. 17m. 2. fur, 1 rd. 4,5 yd. 
468. From 18 yd. 2qr. 1jna. take 2 yd. 1 qr. 2 na. 
12 in. Ans. 16 yd. Oqr. 2na. 15), in. 
469, What is the difference between 1 of 15 bu. 3 pk. 


43 qt. and + of 19 bushels ? Ans. 524 qt. 
10* | 


114 VULGAR FRACTIONS. 


470. From 5 deg. 138m. 6 fur. 14frd. take 138m. 7 + 
fur. 13rd. 4 yd. 24 tt. 
Ans. 5 deg. 69m. 3fur 5 yd. 134 ft. 


MULTIPLICATION OF DENOMINATE NUMBERS. 


- Art. 150. To multiply a denominate number by a 
fraction, 


Rute.—Multiply the given denominate number by the 
numerator of the fraction, and divide the product by the 
denominator. 


Notre.—If the multiplier is a mixed number, reduce it to an improper frac- 
tion ; if compound or complex, reduce it to a simple fraction. 


471. Multiply £13 15s. 9d. by 32. 
Ans. £50 11s. 1d. 
472. Multiply £154 18s. 44d. by 152. 
Ans. £2364 4s, 52; a. 
473. Multiply 13 Ib. u oz. 15 dwt. 16% gr. by 5]. 
Ans. 82 Ib. 1 oz. 14 dwt. Ae or. 
474, Ma Oe ton 19 ewt. 1 qr. 15 1b. by 
Ans. 54 T. 6 ewt. sts sas 
475. What is 73, of 941b.235 13 15 gr. 
Ans. 6 lb.73 25 131 gr. 
476. What is 3 of 31 yd. 2qr. I na. 2 in. 
Ans. 38 yd. 3. qr. 3 na, Og& in. 
477, What is 35, of 17m. 8 fur. 8p. 2h yd. 
Ans, 6m. 3 fur, 20 p. 1242 yd. 
478. Multiply 78 A. 3 BR. 15 sq. p. 15 sq. yd. by 153 
Ans, 12385 A. 1 R. 2 sq. p. 231 sq. yd. 


479. Multiply 118 sol. yd. 22 sol. ft. 1800 sol. in. by 
334. Ans. 3794 sol. yd. 20 aol. ft. 7092, 


‘ 


DIVISION OF DENOMINATE NUMBERS. yy 


480. Multiply 55 bu. 3 pk. 53 qts. by 662. 
Ans, 3728 bu. 1 pk. 73 qt 


481 Multiply 175 da. 13 hr. 222 min. by 11}. 
Ans. 1950 da. 15 hr, 153 min. 


DIVISION OF DENOMINATE NUMBERS. 


Art, 151, To divide a mixed denominate number by 
a fraction, 


Rutze.—Multiply the given denominate number by the 
» fraction inverted. 
482. Divide 3s. 8d. by 2. Ans. 5s. 6d. 
483. Divide £15 10s. 83d. by £. 
Ans. £17 15s, 14d. 
484, Divide 49 bu. 3 pk. 1 qt. by 4. 
Ans, 62 bu. 0 pk. 71 qt. 
485. Divide 16 m. 5 fur. 184 p. by 5%. | 
Ans. 18 m. 4 fur. 112 p. 
486. Divide 31 yd. 1 qr. 84 na. by 4%. 
Ans, 53 yd. 3 qr./28 na. 
487. Divide 67 yd. 1 ft. 61 in by 2 
Ans. 112° yd. 1 ft. 6525 in. 
488, Divide £33 9s. 83d. by 3. 
Ans. £10 9s. 331d. 
489. Divide 14 lb. 11 oz. 15 dwt. 15 gr. by 53. 
Ans. 2 1b. 8 oz. 13 ewt. 18 gy. 
490. Divide 12 tons 13 ewt. 1 qr. 15 1b. by 162. 
Ans 15 ewt. 0 qr. 202 Ib. 
491. Divide 121 1b. 33 23 15 4gr. by 133. 
Ans. 8lb. 93 63 25 33 gr, 
492, Divide 17 yd. 3 qr. 14.na. 74. 
Ans, 2 yd. 1 qr. 24%; na. 


116 VULGAR FRACTIONS. » 


4938. Divide 1555 m. 3 fur. 15 p. 38 yd. by 83, 20° . 
Ans. 464 m. 2 fur. 17 rd. 454°) yd. 


494, Divide 729 A. 3 R. 15 sq. p. 25 sq. yd. by 5%. 
Ans. 126A. 3 BR. 28 sq. p. 25.9% sq. yd. 
495. Divide 341 cu. yd. 17 cu. ft. 1500 cu. in. by 
ATs. Ans. 9 cu. yd. 2 cu. ft. 172123 cu. in. 
496. Divide 31 bar. 2 gal. 3 qt. 14 pt. by 183. 
Ans, | bar. 20 gal. 2 qt. 1332 pt. 
497. Divide 15 bu. 3 pk. 14 qt. by 314. 
Ans. 2 pk. 0124 qt 
498. Divide 25 yr. 45 da. 124 hr. by 142. 
Ans. lyr. 277 da. 222 hr. 
499. Divide 51° 13’ 15” by 714. Ans, 43’ 8", 


PROMISCUOUS EXAMPLES IN DENOMINATE NUMBERS, 


500. A person bought 34 bushels of wheat for £1 13s. 
4d. per bushel, and 54 lb. of tea, at 9s. 10d. per |b.; 
what did they both cost ? Ans, £8 2s. 82d. 


501. A farmer bought 3 bu. 1 pk. 5 qt. of rye for $1 ; 
how many bushels could he buy for $104? 
Ans. 35 bu. 3 pk. 03 pt. 


502. What is the sum of 4 of 10 ewt, 84 qr. and 3 of 
5 tons 12 cwt. 1 qr. 4 lbs? 
Ans. 4T. 3 ewt. 2 qr. 6 Ib. 


503. What. is the difference between $ of 5 sq. m. 
250 A. 3 R. and 34 times 456 A. 3 R. 14 sq. p. 25 sq. 
yds? Ans. 2 sq. m. 254 A. 2 R. 26 sq. p. 243 sq. xe 


504. What is the pe of +2, of 12 gal. 8 qt. 743. of 
19 gal. 3 qt. 1 pt. and 725 of 21 gal. ? 
Ans, 4 gal. 2 qt. 0755 pt. 


Notz.—In the following examples, reduce the given cenominate numbers 
to udenomination, of which the value of a unit is given. 


PROMISCUNUS EXAMPLES DENOMINATE NUMBERS. 117 


505. If 1 hhd. of molasses cost £4 16s. 8d., what will 


124 hhd. cost ? Ans. £60 8s. 4d. 
506. What is the price of 13 ewt. 3 qr. 15 Ib. of sugar, 
at $72 per cent. ? Ans. $102.5114. 
507. What is the price 16 bu. 3 pk. 2 qt. of meal at 
474 cts. per bushel ? Ans. $7.9832 
508. What is the price of 17 T. 15 cwt. 34 qr. of iron 
at 32 per cwt. ? Ans. $1201;. 
509. What is the price of 74 yd. 3 qr. 24 na. of cloth 
at £14 per yd.? Ans. £99 17s. 6d. 


510. If a person sell 29 gal. 3 qt. 1 pt. of wine at 
$25 per gallon, what will he sell the whole for ? 
Ans. $76.3433 
511. If 12 lb. 3 oz. 15 dwt. 6 gr. of gold will bring 
$162 an ounce, how much will the whole come to? 
Ans. $2475.0214. 


512. If 1 acre of land cost £14 12s. 10d., what will 
314 acres cost ? Ans. £456 16s, 44d. 


513. If 3 bushels cost £13 11s. 10d., what will 172 
bushels cost ? Ans. £80 0s. 93d. 


514. If 10 acres cost £489 13s. 11d., what will 714 
acres cost? Ans. £3501 68. 655d. 


515. If 102 lb. of tea cost £4 10s. 4d., and 41 Ib. 
cost £1 17s. 6d., what will be the price of one pound 
of the mixture ? Ans. 8s. 6}2$d. 


516. A grocer mixed sugar worth $7.711 per ewt., 
with an equal quantity of sugar worth $9.514 per ewt., 
what is the price of 7 cwt. of the mixture ? 

Ans. $59.592. 


517. A merchant bought 52 barrels of pork at £1 19s. 
24d. per barrel; 18+ barrels of beef at £2 1s. 34d. per 
barrel, and 124 barrels of fish at 19s. 54d. per barrel; 
what did they all cost ? Ans. £60 8s. 113d. 


118 VULGAR FRACTIONS, 


518. If one acre of ground cost £173, New York cur- 
rency, how many dollars will 12 A. 2 Rh. 20 sq. p. cost? 
Ans, $560.28. 


519. Received from Lowell, a piece of muslin, con. 
taining 431 yd., and marked to be sold at 1s. 6d. a yard, 
New England currency ; how much New York currency 
a yard is the muslin, and what is the value of the whole 
in Federal money ? — A 2s. a yard. 

. ns. : 

$10.814 total value. 


520. Received from Philadelphia, 4 pieces of cloth, 
each piece 393 yd., and marked ‘£1 7s. ow. a yard; how 
much a yard, New York currency will that be, and 
what will be the total value in Federal money ? 


£2 a yard 
eee $795 total value. 


521. If wheat cost £14, New York currency a bushel, 
how many bushels may be bought for $108.2812 ? 
Ans. 28 bu. 3 pk. 4 qt. 


DECIMAL FRACTIONS. 119 


DECIMAL FRACTIONS. 
Art. 152. What 1s a Decimal Fraction 2 


Bis a fraction whose denominator ts a unit with as 
many ciphers annexed as there are places of figures in the 
numerator. 


Art. 153. How are decimal fractions written 2 


They are written like whole numbers, having a point to 
the left of those figures that compose the decimal, the 
denominator being understood. 


Art. 154. Why can they be written like whole num 
bers ? 


Because, from the nature of their denominators they 
follow the same law, thatis, they decrease in a tenfold ratio 
to the right, and increase in the same ratio to the left. 


Art. 155. What is the first figure to the right of the 
point called ? 


Tenths. 


Art. 156. What are the succeeding ones called ? 


~ The second is called hundredths, the third, thousandths, 
the fourth, ten thousandths, de. 


Art. 157. What effect is produced on the value of a 
decimal by annexing ciphers ? 


There is no effect produced. 
Art. 158. Why ? 


Because when a cipher 1s annexed to a decimal, there 
must be one annexed to the denominator understood, which 
increases both numerator and denominator in a ten-fola 
rato, and therefore docs not alter the value of the frgction. 


Notr.—For a like reason when the ciphers are rejected from the right of a 
decimal fraction, there is ne alteration in the value of that fraction. 


120 DECIMAL FRACTIONS. 


Art. 159. What effect is produced o. tne value of a 
decimal by prefixing ciphers ? 


It decreases the value in a ten-fold ratio for each cipher 
prefixed. 


Art. 160. Why ? 


Because when a cipher is prefixed to a devimal there 
must be one annexed to the denominator understood, a pro- 
cess which without altering the value of the numerator, 
tncreases the value of the denominator ten-fold, and there- 
fore decreases the value of the fraction ten-fold. 


Art. 16]. To reduce a decimal into a vulgar fraction, 


Ruiz.— Under the decimal fraction place its denomina- 
tor, and reduce the vulgar fraction thus formed to its 
lowest terms. 


1. Reduce .1 to a vulgar fraction. Ans. 74. 
2. Reduce .2 to a vulgar fraction. Ans. #. 
3. Reduce .3 to a vulgar fraction. Ans. 335. 
4. Reduce .4 to a vulgar fraction. Ans, 2. 
5. Reduce .5 to a vulgar fraction. Ans. }. 
6. Reduce .25 to a vulgar fraction. Ans, 3}. 
7. Reduce .85 to a vulgar fraction. Ans. 35. 
8. Reduce .40 to a vulgar fraction. Ans: 12: 
9. Reduce .50 to a vulgar fraction. An® 4. 
10. Reduce .01 to a vulgar fraction. Ans. ;4;- 
11. Reduce .075 to a vulgar fraction. Ans. 7. 
12. Reduce .005 to a vulgar fraction. Ans. x45. 


13. Reduce .0025 to a vulgar fraction. Ans. 745. 
14, Reduce .8015 to a vulgar fraction. Ans. 1693s 
15. Reduce .68375 to a vulgar fraction. Ans. 344. 


ADDITION. 121 
16. Reduce .265625 to a vulgar fraction. Ans. 44. 
17. Reduce .82 to a vulgar fraction. Ans. 2. 
18. Reduce .162 to a vulgar fraction. Ans. 4. 
19. Reduce .834 to a vulgar fraction. Ans. 4. 
20. Reduce .482 to a vulgar fraction. Ans. 73 
21. Reduce .561 to a vulgar fraction. Ans. 7%. 
22. Reduce .2252 to a vulgar fraction. Ans. {°3-. 
23. Reduce .01875 to a vulgar fraction. Ans. 735. 
24. Reduce .105 to a vulgar fraction. Ans. 345. 
25. Reduce .02 to a vulgar fraction. Ans. so: 
26. Reduce .04 to a vulgar fraction. Ans. ar: 
27, Reduce .05 to a vulgar fraction. Ans. 35. 
28. Reduce .75 to a vulgar fraction. Ans, 3. 
29. Reduce .125 to a vulgar fraction. Ans. 4 
30. Reduce .45 to a vulgar fraction. Ans, 25. 
31. Reduce .025 to a vulgar fraction. Ans. zy. 
32. Reduce .325 to a vulgar fraction. Ans, 43, 
33. Reduce .875 to a vulgar fraction. Ans. 2. 
34. Reduce .525 to a vulgar fraction. Ans, 21, 
35. Reduce..625 to a vulgar fraction. Ans. 2. 
36. Reduce .875 to a vulgar fraction. Ans. Z. 
37. Reduce .0125 to a vulgar fraction. Ans. 44 
88. Reduce .0375 to a vulgar fraction. Ans, 3%. 


—— 


ADDITION 


Arr. 162. To add decimal fractions, 


Rutz.—Place the whole numbers under each other, «8 
in simple addition, and the decimals, tenths under tenths, 
hundredths under hundredths, thousandths under thow 

11 


122 DECIMAL FRACTIONS. 


sandths, d&c.; commence at the right hand column of 
decimals, and add as in simple addition, and place the point 
we the answer under the point in the numbers added. 


Nortr.—In reading a mixed decimal, let the word and indicate the placecf . 
tke point, thus 216.074, two hundred sixteen and seventy-five thousandths. 


(39.) (40.) (41.) 
Add, 1.151 15.717 888.017 
13.29 1.4 672.45 
116.283 99.006 1112.7586 
9.0275 186.995 8672.048711 
61 11 24.0009 
” 110.3615 464,271 11369.27521 1 
(42.) (43.) (44.) 
B15 8 1.2 
0375 087 17 
00375 626 498 
9 8885 8.2461 
4.65 49628 98,.38659 
} 008 
(45.) (46.) (47.) 
29.5 83.575 38649.25 
16.75 1.082 463.275 
128,125 346.1261 386.275 
14.25 59.86491 496.1375 
16.875 596.30802 507.18 
486.0625 49.591 29.1636 
3511.775806 8.37625 9.1807 
299.483 499.38572 2,008 


ADDITION, 123 


48. Add four tenths; five ard eighteen hundredths ; 
seven hundred twenty-one, and twelve thousandths ; 
seven hundred seventy-five thousandths; seven, and 
seventy-five thousandths ; three, and four hundred eighty- 
six ten thousandths; eight thousand fifty-seven, and one 
vundred as eight hundr ed thousandths. 

Ans, 8794.49218. 


49. Add sixteen thousandths; four hundredths; five 
tenths; seven thousandths; ninety-four miillionths ; 
eleven, and four hundredths ninety-nine, ten thousandths ; 
twelve, and three hundr ed | seventy-five ten millionths. 

Ans. 23.6130315. 


50. Add three thousand four hundred eleven and 
twenty-seven hundredths, 600 and eighty-six ten thou- 
sandths; eight millions, seven hundred ninety-five, and 
two hundred eighteen ten thousandths; nine hundred 
ninety-seven, and six hundred fifteen "hundred thou- 
sandths, Ans. 8005803.80655 


51. Add 54, 331 thousandths, 679, 374 neuen) 
6073, 56 hundredths, 30045, and 649 thousandths. 
Ans. 45852.2792. 
52. What is the sum of 91.003+ 16.4591 + 700.05 +- 
160.0047 1+ 900.0006 + 0815? Ans. 1867.54891. 


58. What is the sum of 305.8675+300.008+745. 
68375 + 75.0075 + 6675.00911+ 675 + 1000 ? 
Ans. 9776.57586. 


54, What is the sum of 316-++1569-+69806+ 3154.6 

+ 254.08 + 16.098 + 4986+ .00367 ? 
Ans. 80101.78167. 

55. What isthe sum of 1886.7900675 -- 9000.067586 

+ 27659.59632+ 576496.0049 + 9865711.909 + 18.750- 
06275 2 Ans. 10480773. 11'7938625. 


124 DECIMAL FRACTIONS. 


SUBTRACTION. 
Art. 163. To subtract decimal fractions, 


Ru.e.— Place the less number under the greater, whole 
numbers under each other, and the decimals, tenths under 
tenths, hundredths under hundredths, thousandths under 
thousandths, &c. ; commence at the right hand and sub- 
tract as in simple subtraction, and place the point under 
the point ; if the subtrahend contain more decimal figures 
than the minuend annex, or conceive to be annexed, as 
many ciphers to the minuend as will make the number of 
decimal figures in rt equal to those in the subtrahend. 


(56.) (57.) (58.) 
From —.298.789 127.334 94.86071 
Take 196.493 55.827 27.861 
RoR Re ae 
102.296 71.507 66-99971 
(59.) (60.) 61.) 
2684.11 986.444 2.867 
199.8637 98.6438 9965 
2484,2463 
(62.) (63.) (64.) 
148.21 5.5 6754.298 
99.118 4.875 24.17 
(65.) (66.) (67.) 
2864.271 075 79.88623 


881.896001 0375 78.912 


OS 


SUBTRACTION, 125 


(68.) (68.) + (70.) 


1936.54 8.1 45.37508 
937.86101 DOLE 23.96 109 


71, From seventeen and two hundredths, take seven 
and twenty-five hundredths, ANS). Te 


72. From six hundred sixty-one, take ninety-five and 
seven hundred twenty-one ten thousandths. 
Ans. 565.9279. 


73. From twenty-five thousand, take one and seventy 
seven thousandths. Ans. 24998.928. 


74. From three hundred twenty thousand and forty 
five ten thousandths, take seventy-nine thousand eight 
hundred and seven and six hundred forty-nine millionths, 

Ans. 240193.003851. 


75. From one, take one-thousandth. AOS. .099, 


76. From ten, take three-millionths. 
| Ans, 9.999997. 


77. What is the difference between six, and sixty 
seven hundred thousandths ? Ans, 5.99933. 


MULTIPLICATION. 
Art. 164. To multiply decimal fractions, 


“‘ 


Rurz.— Multiply as in whole numbers, and point off in 
the product as many decimal figures as there are in both 
multiplier and multiplicand., 

78. Multiply .1 by .1. Ans. .01, 

79. Multiply .2 by .2. Ans. 04. 

80. What is the product of 01 by .1? Ans, .001. 

Vi 


” 


126 DEUIMAL FRACTIONS, 


81 Multiply .003 by .04. Ans. .00012. 
82. Multiply .00014 by 1500. Ans. 21. 
83. What is the product of .025 by 7000 ? 

Ans. 175. 
84. Multiply 38.4 by 16.7. Ans. 641.28. 
85. Multiply 275 by 4.75. Ans. 1806.25. 
86. Multiply 14.25 by .375. Ans, 5.84875. 


87. Multiply 78.248 by 1.025. Ans. 80.199075. 
88. Multiply 146.05 by 128.6 Ans. 18782.03. 
89. Multiply .34 by .075. Ans. .0255. 
90. Multiply .565 by .16. Ans. .0904. 
91. Multiply .04685 by .0081. Ans. .00037508. 
92. Multiply 701.005 by 60.06. Ans. 42102.3603. 
93. Multiply 456.05 by 3.81. Ans, 1744.8911, 
94. Multiply 308.25 by .0773. Ans. 25.889374. 
95. Multiply 27.0822 by 14.3. Ans. 386.5701. 


96. Multiply 880.06 by 224. Ans. 8665.364. 
97. Multiply 24.073 by .125. Ans, 3.009284. 
98. Multiply 75 by .833. Ans. 25. 
99. Multiply 456.87 by .0662. ~ Ans. 30.458. 


100. Multiply 798.007 by .00S3. Ans. 6.650058. 


Arr. 165. To multiply a decimal by 10, 100 
1000, &e., 


Rurxe.—Move the decimal point as many places to the 
right as there are ciphers to the right of the unit of the 
multiplier, and annex ciphers if necessary. 


101. Multiply 375.456 by 10. Ans, 8754.56. 
102. Multiply 1845.267 by 100. Ans, 134526.7. 
103. Multiply .00~5 by 1000. Ans. 7.5. 


MULTIPLICATION, T27 


104. Multiply 17.5 by 100. | Ans. 1750. 
105. Multiply 3.05 by 10000. Ans. 30500. 
106. Multiply 45.06 by 114. Ans. 5002. 
107. Multiply 850.77 by 1428. Ans. 50110. 
108. Multiply 7.0852 by 100. Ans. 703.52. 


Nore.—Cents are hundredths and mills thousandths of a dollar, and there- 
fore are decimal fractions, 

Since the smallest coin used in Federal Money is the cent, it is nasal in 
actual transactions, if there be more than two decimals in "the answer, to 
increase the cents one, when the third decimal is 5 or more, and reject all ex- 
cept the two decimals that represent the cents; and when the third is less 
than 5, to reject it and the others to the right of it; but for the present the 
entire answer will be set down for the sake of practice. 


109. What will 44.5 gallons of oil cost at $1.875 per 


gallon ? Ans. $61.1875. 
110. What will .075 of an acre cost at $3001 per 

acre ? Ans, $22.5182. 
111. What will 75.5 yd. of muslin cost at $.123 a 

yard ? . Ans. $9.4372, 


112. How much will a person have to pay for 36.25 
lb. of coffee at $.162 a pound ? 
Ans. $6.04162. 


« 113. If one bushel of wheat cost $3.15, what will 
710.05 bu. cost ? Ans, $2236.6575. 


114. If $371 will buy 1 acre of land, how much will 
175.315 acres cost ? : Ans, $6574,3122. 


115. If you can buy 13.44 lb. of sugar for $1, how 
many pounds can you buy for $17.33}. 
Ans. 282.96 Ib. 


116. If 1 tun of wine cost $301.75, what will 12.8375 


tans cost 2 Ans. $8722.840625. 
117. The factors of a number are 31.025 and 7.31; 
what is the number 2 Ans, 226.79275. 


118. A field is 85.108 rods one way, and 142.9 the 
other ; how many square rods does it contain ? 
Ans, 5016.2187 sq. rd. 


128 DECIMAL FRACTIONS. 


119. A field is 45.001 feet wide and 37.4 yards long ; 
how many square feet does it conta n ? 
Ans. 15147.8366 sq. ft. 


DIVAISLONS 


Art. 166. To divide decimal fractions, 


Rutze.—Divide as in division of whole numbers, and 
point off in the quotient as many decimal figures as those 
in the dividend exceed those in the divisor. 

If the decimal figures in the divisor are of the same 
number as those in the dividend, the quotient will be a 
whole number. 

If there be more decimal figures in the divisor than in 
the dividend, previous to dividing, annex as many ciphers 
to the dividend as will supply the deficiency, and more if 
necessary. 

NotTE.—When the division is not exact, ciphers may be annexed to the 
dividend, and the quotient continued to any number of decimal figures ; four 
is generally suflicient. 

120. Divide 84.75 by 2.5. Ans. 13.9. 

121. Divide.461.03 by 21.4. Ans, 21.5434. 

122. Divide 3467.007 by 9.09. Ans, 381.4089. 

123. Divide 1728.6475 by 18.75. Ans. 92.1945. 


124. Divide 97481.06875 by 91.375. 
Ans. 1066.825. 


125. Divide 341.452 by 3.025. Ans. 112.8766. 
126. Divide 7551.475 by 7.222. Ans. 

127. Divide 16.025 by .045. Ans, 356.11113. 
128. Divide .9375 by .075. Ans. 12.5. 
129. Divide .0869725 by 38.04. Ans. .00228. 
130. Divide .00643875 by 4.0275 Ans. .00159. 
131. Divide 9822.15 by 6.275, Ans. 1485.6, 


DIVISION. 129 


182. Divide 7231.5 by .4751. Ans. 15221.0061+. 


133. Divide 480 by 3.12. Ans. 153.8461. 
134. Divide 7650 by .6575. Ans. 12000. 
135. Divide 9150.9 by .0885. Ans. 103400. 
136. Divide 324 by 6400. Ans. 050625. 
187. Divide 18 by 288. ' Ans. .0625. 
188. Divide 23 by 14375. Ans. .0016. 


139. Divide 1728.3508 by 188. Ans, 91.5009. 
140. Divide 16711.259 by 253. Ans. 649.88229+. 
Art. 167. To divide a decimal by 10, 100, 1000, &c., 


Ruiz.—-Move the decimal as many places to the left as 
there are ciphers to the right of the unit of the divisor, pre- 
fixing ciphers if necessary. 


141. Divide 188.475 by 10. Ans. 18.8475, 
142. Divide 1936.25 by 100. Ans, 1928, 
148. Divide 812.5 by 100. Ans, 84. 
144. Divide 1496.04 by 1000. Ans. 1.49604. 
145. Divide 74.96 by 1000. Ans. .07496. 
146. Divide .5 by 100. Ans. 005, or 32q-.: 
147. Divide 41.1 by 100,000. Ans. .000411., 
148. Divide 791.66 by 3334. Ans. 2.37498. 
149. Divide 675.025 by 934. Ans, 74,25275. 
150. Divide .012 by 1114. Ans. .000108. 
151. Divide .125 by 4000. Ans. .00003125. 
152. Divide .64 by 8000. Ans. .00008. 


153. What is the quotient of .0186 divided by 2400? 
Ans. 00000775. 


Art. 168. To reduce a vulgar fraction to a decimal, 


Ruie.—Annex ciphers lo the numerator, divide by the 


130 


DECIMAL FRACTIONS. 


denominator, and point off thedecimals in the quoteent as in 
division of decimal fractions. 


NotEe.—When the denominator of the vulgar fraction is 2or 5, or their mul: 


tiples, the decimal fraction will come out exact. 


154. 
155. 
156. 
157. 
158. 
159. 


160. 
16t: 
162. 
163. 
164. 
165. 
166. 


167. 
168. 


172. 


a decimal fraction. Ans. .8. 


ct 
je) 


Reduce 
a decimal fraction. Ans, .875. 


ot 
io) 


Reduce 
Reduce a decimal fraction. Ans. .5. 


a decimal fraction. ANS. 208 


cr 
co) 


Reduce 


mlco mle toll coky Crim 
cr 
co) 


a decimal fraction. ADS. #4): 


ou 
oO 


Reduce 


Reduce ;%, to a decimal fraction. 
Ans, .1875. 


Reduce 3 to a decimal fraction. Ans. .625. 


Reduce ;% to a.decimal fraction. Ans, .45. 
Reduce }2 to a decimal fraction. Ans. .9375. 
Reduce 5*; to a decimal fraction, Ans, .16. 
Reduce 42 to a decimal fraction. Ans, .68. 
Reduce 22 to a decimal fraction. Ans. .58. 
Reduce 743 to a decimal fraction. 


Ans. .0078125 
Reduce 3), to a decimal fraction. Ans. .03125. 


Reduce 73; to a decimal fraction. 


Ans. .016. 


. Reduce 7,355 to « decimal fraction. 


Ans. .00075. 


. Reduce 2 of i; of 14 to a decimal fraction. 


Ans. .04, 


. Reduce =% of 74 of 44 to a decimal fraction. 


8 it 


Ans. 5.8109375. 
3 
Reduce s to a decimal fraction.. 


Ans. 58125, 


REPEATING DECIMAL FRACTIONS. 13! 


1 
173. Reduce ee to a decimal fraction. 
s 
Ans. 3125. 
4 
174, Reduce 3 to a decimal fraction. 
4 


Ans. .0576. 
175. Reduce 2 to a decimal fractions. Ans. .07, 


176. Reduce 4% to a decimal fraction, 
Ans. .02578125. 


Art. 169. What are repeating decimal fractions ? 


They are decimal fractions having the same Jigures con- 
finually repeated, 


Art. 170. From what do they arise ? 


They arise from changing into decimal fractions, those 
semple vulgar fractions whose denominators are prime num- 
bers or multiples of prime numbers, and whose terms are 
prime to each other, ° 


Notre.—-There are two exceptions to this, viz., when the denominators are 
2 and 5. 


The figure or figures repeated are called the repetend. 


_ For abbreviation in writing repeated decimal fractions, a single point pla- 
ced over a figure indicates that the figure is to be continually repeated. 


When there is a series of two or more figures, two points, one “placed over 
the first and the other over the last figure, indicate that the series is to be con 
tinually repeated. 


177. Reduce 4 to a decimal fraction. 
Ans. .883333-+ or .3. 


178. Reduce 2 to a decimal fraction. 
Ans. .666666-+ or 6. 
179 Reduce $ to a decimal fraction. Ans. .4. 
7 
9 


180. Reduce Z to a decimal fraction. Aus. .%, 


182 DECIMAL FRACTIONS. 


181. Reduce ;4, to a decimal fraction. 
Ans. .863636-+or 36. 
182. Reduce =° Bs to a decimal fraction. Ans. 15. 
183. Reduce 3% to a decimal fraction. 
Ans, 518518-+or 513. 
184, Reduce 585, to a decimal fraction. neq. 
Ans. .64356435 -++ or .6435. 
185. Reduce 4 to a decimal fraction. : 
Ans. .142857. 
186. Reduce %; to a decimal fraction. 
Ans, .384615. 
187. Reduce = 3 to a decimal fraction. 
Ans. .416666-+ or .416. 
188. Reduce 54 to a decimal ASehon 
| Ans. .2916. 
189. Reduce 2 to a decimal fraction. Ans. .045. 
190. Reduce +4%% to a decimal fraction. 
Ans. .1118. 
191. Reduce Nae to a decimal fraction, 
AtT | 


Ans. .53. 


Arr. 171. To reduce a repeating decimal fraction to a 
vulgar fraction, 


Rutzt.— Write as many 9’s under the repetend as there 
are figures in the repetend. 


192. Reduce .5 to a vulgar fraction. Ans. 3 
193, Reduce .6 to a vulgar fraction. Ans. 2. 
194. Reduce .27 to a vulgar fraction. Ans. =. 


195. Reduce .036 to a vulgar fraction. Ans. 747. 


DIVISION, 133 


196. Reduce 7227 to a vulgar fraction. Ans, 773. 


197. Reduce .23 to a vulgar fraction. 
Ans. .24 or 3%. 


198. Reduce .416 to a vulgar fraction. Ans. 4°. 
199. Reduce 2354 to a vulgar fraction. 


200. Reduce .06603 to a vulgar fraction. 
Ans. ri 00° 


201. Reduce .428571 to a vulgar fraction. ‘ 
Ans. 2 


202. Reduce .¢76023 to a vulgar fraction. 
Ans. 35. 


NotEe.—Addition, subtraction, multiplication and division may be perform 
ea upon repeating decimal fractions by reducing them to equivalent vulgar 
fractions; in the first three rules the error will be but small. if they are car- 
ried out to five or six decimal figures and then operated upon. But when 
a repeating détimal fraction is a divisor, the repecend should be reduced 
to an equivalent vulgar fraction; for then the errorin the quotient is very 
sensible. 

When the number of articles and their value are known, how can 


the price of a single article be found? (Art. 53.) 


When the value of a single article and the value of several arti- 
cles are known, how can the number of articles be found ? (Ar. 54.) 


Nove.—The divisor and dividend must be of the same denomination, exe 
cept when the value of a single article is to be found. 


203. If 17 lb. of tea cost £12.375, what will-one pound 


cost 2 Ans, £.7279,-+- 
204. If 20 bushels of wheat cost $18.542, what will 
one bushel cost ? Ans. $.9271. 
205. If a man can earn $500 in 13.125 weeks, how 
much can he earn in one week ? Ans. $38.095. + 
206. If flour cost $5.75 per barrel, how many barrels 
ean be bought for $1035 ? Ans, 180 barrels. 


207. If 100 pounds of sugar cost $7.25, what will one 
pound cost ? Aus. $.0725, 


1384 DECIMAL FRACTIONS. 


208. If 1000 acres of land cost 175861.04, what will 


one acre cost ? Ans. $1'75.86104. 
209. If one acre cost $500, how many acres can be 
bought for $3785.455 ? Ans. 7.57091 acres. 
210. If the freight of 257.5 Ib. be $1,what will be the 
freight on a ton ? Ans. $7.767. 
211. If 23 lb. of tea cost $1, how much will 3 cwt. 
ligre 15, 5 Ib. cost 2 Ans. $123.818. 


212. At 12 shillings per gallon, how many gallons can 
be bought for £37. 15.75s? « Ans, 566.8125 gal. 
213. If 75.0325 cords of wood cost $600, what will 


one cord cost ? Ans. 7.9965. 
214. If 19.75 yards of cloth cost $83.25, how much 
will one yard cost? Ans, $4.215. 


PROMISCUOUS EXAMPLES? 


215. If a horse cost $175.511, a wagon $59.875, and 
the harness $123, to what will the eehite amount 2 
Ans. $247,9375. 


216. Ifa person have $1521, and should loose $75.625, 


how much would he have left 2 Ans. 76.875. 
217. A person earned $14.662 a-day, for 51.5 days ; 

how much did he earn altogether ? Ans. $462. 

- 218. If one yard of cloth cost $4.50, what will 7.125 

yards cost ? Ans. 82.0625. 

219, If one bushel of wheat cost $.9875, what will 28 

pushels cost 2 Ans. $26.25. 


220. For one dollar a boy bought 250 apples; how 
many would that be for $6.64? Ans. 1660 apples. 


221. If 3 barrels of flour cost $10.125, what will 100 
barrels eost 2 Ans. $337.50. 


222. If 5.1 acre cost $1501.35, what will 10 acres 
enst ? Ans, $2943.82. 


' PROMISCUOUS EXAMPLES, 185 


- 


223, If 4 bottles of equal size contain 5.805 pints, how 
much will 1000 bottles contain 2 Ans. 1451.25 pt. 


224. 25 barrels of beer cost £64.0625 ; how much 


will 14.48 barrels cost ? Ans L3TilOe: 
225. If 1000 bushels of rye cost $250, what will 2.5 
bushels cost 2 Ans. $.625. 
226, If 10 tons of hay cost $42.625, what will 88.4 
tons cost ? | Ans, $163.68. 
227. If 100 head of cattle cost $7211.50, what will 
one cost ? Ans.272i 


228. If 7.5 yd. of muslin cost 15 shillings, how many 
yards can be bought for £13.4482 Ans. 134.48 yd. 
229. If 120.06 bushels of potatoes are raised upon 3 
acres of land, how many acres would it take to raise 
4580.64 bushels ? Ans. 114.458 acres. 
230. If one ounce of gold be worth $18.42, how much 
will $38575.875 worth of gold weigh? 
Ans, 2094.288. 02. + 
231. If .65 of a pound of sugar cost $.08125, how 
many pounds can be bought for $100? Ans. 800 lb. 


232. If a man can travel 32.445 miles in 7 of g day, 
how far can he travel in 8654 days? Ans. 13543.47 
233. A boy can earn 1.71875 shillings in 2.5 days; 
how much can he earn in 12.32 days? Ans. 8.47s. 
234. What will 36.48 yards.of cloth cost, when 14.25 
yards cost $21.375 ? Ans. $54.72. 
235. If 2 lb..of sugar cost $.1875, what will 10 lb, 
cost ? Ans. $.9375, 
236. If 3.25 yd. cost $15.375, how much will 100 yd. 
cost ? Ans. $473.07;°;. 
237. What is the price of 2850 shingles, at $21.75 per 
thousand ? Ans. $61,982. 
238. What will 17 cwt. 2qr. 7.5 1b. cost, at $6.75 
per hundred pounds ? Ans. $118.68. 


136 DECIMAL FRACTIONS, 


239. If 17.05 bushels cost $13, what will 100 bushels 
cost 2 Ans. $76.24. 


240. If you can buy 1314 lb. of coffee for $2.50, how 
many pounds can you buy for $325.50 ? 
Ans. 172437 Ib. 


241. If 100 chaldrons of coal cost £12.875, what will 
38.25 chaldron cost ? Ans. £4.'7834. 


242, How many yards of muslin can be bought for 
£19 10s. 6d., at 9.5d. for 2.875 yards ? 
Ans, 11714 yd. 


REDUCTION. 
& 
Art. 172. To reduce a denominate decimal from a 
higher to a lower denomination, 


Ruiz.—Multiply the given denominate decimal by as 
many of the denomination neat lower as will make a unit 
of the given denomination ; multiply this result as before, 
and so proceed until the decimal is reduced to the denomt- 
nation required, 

NotE.—In the course of the operation, the products may be kept entire, or 
mm each product the whole number may be reserved and the decimal portion 
be multiplied; at the end, collect all the whole numbers, commencing at the 


highest denomination, and arrange them in a horizontal row with the last 
decimal annexed to the lowest denomination. 


243. Reduce .8475 £ to pence. 
Ans, 83.4d. or, 6s. 11.4d. 


244. Reduce .9375 lb. to grains, Troy Weight. 
Ans. 5400 gr. or, 11 oz. 5 dwt. 


245. Reduce .11875 tons to pounds. 
Ans. 237.5 lb. or, 2 ewts. 1 qr. 12 Ib. 8 oz. 


246. Reduce.9995 Ib. Apothcaries’ weight to grains, 
Ans. 5757.12 gr. or, 113 73 259 17.12 gr. 
247. Reduce .5725 yd. to inches, cloth measure. 
Ans, 20.51 in. or, 2 qr. 1 na. 0.36 in, 


REL UCTION. 137 


248. Reduce .90125 m. to poles. 
Ans. 288.4 p, or, 7 fur. 8.4 p. 


249, Reduce .04925 m. to feet. 
Ans, 260.04 ft. or, 15 p. 4 yd. 0.54 ft. 


250. Reduce .0175 A. to its value in lower denomina- 
tions. Ans. 2 sq. p. 24 sq. yd. 1.8 sq. ft. 


251. Reduce .00525 cu. ft. to inches. 
Ans. 9.072 cu. in. 


252. Reduce 5.125 ‘hhd. to its value in lower denomi- 
nations. Ans. 5 hhd. 7 gal. 3 qt. 1 pt. 


253. Reduce 3.2225 chaldrons to its value in lower 
denominations. Ans. 3 ch. 7 bu. 0 pk. 3.84 qt. 


254. Reduce .7725 wk. to its value in lower denomi- 
nations. Ans. 5 da. 9 hr. 46 min. .48 sec. 


255. Reduce 3.4629° to its value in lower denomina- 
tions. Ans23? 27446.447, 


Art. 173, To reduce a denominate number to the 
decimal of a higher denomination, 


Rute.—/f necessary, annex ciphers to the given 
denominate number and divide by as many of itsown denomi- 
nation as it takes to make a unit of the next higher, and so 
proceed until -the number is reduced to the denomination 
required, the quotients being carried out as in division of 
decimals. 


256. Reduce 3d. to the decimal of a shilling. 
Ans. .25s. 

257. Reduce 11d. to the decimal of a shilling. 
Ans. .125s. 

258. Reduce 6 gr. to the decimal of an ounce. 
Ans, .0125 oz, 

259. Reduce 8 oz. to the decimal of pound Troy. 
Ans. .25 lb, 
le? 


138 DECIMAL FRACTIONS. 


260. Reduce 8 dr. to the decimal of a pound Avoir: 
dupois. Ans. .03125 Ib. 


261. Reduce 25 Ib. to the detimal of a ton. 
Ans. .0125 T. 


262. Reduce 3} Z to the deeimal ofa pound. 
Ans. .27083 lb. 


263. Reduce 3.25 na. to the decimal of a yard. 
Ans. .208125 yd. 


264. Reduce 4.0125 feet to the decimal of a rod. 
Ans, .24318 ft. 
265. Reduce 8% feet to the decimal of a furlong. 
Ans. .013257 fur. 
266. Reduce 75 sq. ft. to the decimal of a square 
yard. Ans. .07 sq. yd. 


267. Reduce 45 sq. yd. to the decimal of an acre. 
Ans. .009297 A. 


268. Reduce 24 pt. to the decimal of a gallon. 
Ans. .2916 gal. 
269. Reduce .45 pk. to the decimal of a bushel. 


Ans. .1125. 
270. Reduce 122 days to the decimal of a year of 
3651 days. Ans. .03388 yr. 


271. Reduce 33 ft. to the decimal of a fathom. 
Ans. .625 of a fathom. 


272. Reduce 9 sheets to the decimal of a ream. 
Ans. .01875 of a ream. 


2738. Reduce 75.125 lb. to the decimal of a barrel of 
pork, Ans. .875625 bbl. 


274, Reduce 21 inches to the decimal of a mile. 
Ans. -.0003314 m. 


ao 
REDUCTION OF DENOMINATE NUMBERS. 139 


REDUCTION OF DENOMINATE NUMBERS. 


Art. 174, To reduce denominate numbers containing 
several denominations, to a decimal, 


Ruite.—Commence at the lowest denomination and 
reduce it to the decimal of the next higher, and to this 
decimal prefix the next higher denomination as a whole 
number, reduce this to the decimal of the next higher deno- 
mination ard prefix the next higher denomination ; so 
proceed tll the number is brought to the decimal required, 


275. Reduce 3s. 6d. to the decimal of a pound. 
Ans. £.175. 


276. Reduce £14 17s. 3d. to the decimal of a pound. 
Ans. £14.8625. 


277. Reduce 5 oz. 13 dwt. 12 gr. to the decimal of a 


pound. | Ans, .472916 Ib. 
278, Keduce 15 cwt. 8 qr. 21 lb. to the decimal of a 
ton. Ans, .78875 T. 
279. Reduce 156 Ib. 45 131510 gr. to the decimal 
of a pound. Ans. 156.3489583. 
280. Reduce 3 qr. 1 na. 12 in. to the decimal of an 
E. E. Ans. .675 E. E. 


281. Reduce.7 m. 7 fur. 1 p- to the decimal of a mile? 
Ans. 7.878125 m. 


282. Reduce 2 fur. 18 rd. 4.4 yd. to the decimal of a 


league. Ans. .0977083. 
283. Reduce 5 A. 3 R. 21 sq. p. to the decimal of an 
acre. Ans. 5.88125 ae. 
284. Reduce 3 R. 1 sq p. 18 sq. yd. to the decimal 
of an acre. Ans. .759969 ac 
285. Reduce 290 cu. in. to the decimal of a ton of 
round timber, Ans. .004192 T. 
e 


140 DECIMAL FRACTIONS. 


286. Reduce 3 qt. 1.75 pt. to the decimal of a hhd. 
Ans. .015376 hhd.+- 


287. Reduce 14 bu. 32 qt. to the decimal of a chal- 


dron. Ans. .4410156. 
288. Reduce 14° 15’ 222” to the decimal of a de- 
eree. Ans. 14.25616°. 


289. Reduce 3 da. 123 sec. to the decimal of a week, 
Ans. .428592 wk.+ 


290. Reduce 1 quire 9 sheets to the decimal of a bun- 


dle. Ans. .084875 of a bundle. 
291. Reduce 15 lb. 10 oz. 8 dr. to the-decimal of a 
ton. Ans. .0078282 T. 


292. Reduce 11 pounds to the decimal of a ton. 
Ans. .0055 T. 


2938. Reduce 42 inches to the decimal of a mile. 
Ans. .0006624 m. 
294, Reduce 6 feet to the decimal of a mile. 
Ans. .001186 m. 
295. Reduce 411 sq. ft. to the decimal of an acre. 
Ans. .009435+ A. 


296. Reduce 75 sq. yd. to the decimal of a square 
mile. Ans. .000242 sq. m. 


ADDITION OF DENOMINATE NUMBERS. 
Arr. 175. To add denominate decimals, 
WtuLe.—Leduce the given quantities to the decimal: of 
the same denomination and add as in addition of decimals 


201: Add: £,25, £5, .1 58.) ands,67 os. 
Ans. 16s, 73d. 
298. Add £38.125, £5.15, 3.25s. and 4.25d. 
Ans. £8. 9s. 14d. 


299. What is the sum of .334 lb., .5 1b., 7.5 0z., 5.75 
dwt. and 11 gr. ? Ans. | lb. 5 0z. 16 dwt. 5 gr, 


ADDITION OF DENOMINATE NUMBERS. 14] 


300. What is the sum of 3.05 T., 64 cwt., 3.025 
ewt., and 1.2 qr.? Ans. 3 T. 10 cwt. 2 qr. 74 lb. 


301. Add together .'7125 m., 6.4 m., 3.75 fur., and 
47 rd Ans. 7 m. 4 fur. 30.11 rd. 


302. Add together 13.625 A., 1.0875 A., 3.25 R., 
and 19.05 sq. p. Ans. 15 A. 2 R. 15.05 sq. p. 


303. What is the sum of 3.334 bhd., 15.5 gal., and 
3.165 qt. ? Ans. 3 hhd. 37 gal. 1.165 qt. 


304. What is the sum of 75.02 bu., 16.625 bu., 
3.47 pk., and 4.45 qt.? Ans. 92 bu. 2 pk. 4.85 qt. 


305. What is the sum of 45.655 da., 38.333 min., 
-45 min., and 16.15 sec. ? 
Ans. 45 da. 16 hr. 17 min. 15.15 sec. 


306. Add .75 Ib. Troy weight, .35 Ib., 375 oz., and 
2.125 02. Ans. 1 lb. 3 oz. 14 dwt. 
307. Add’ 2375 T., 875 1.; 3.125 ewt., 14.5. cwt:, 
15 lb., and 13.5 lb. Ans. 2 T..2 cwt. 3 qr. 16 lb. 
308. Add 145.75 lb. apothecaries’ weight, .8375 Ib 
663% 3, 3.5 3, 1.833 3, and 19.875 gr. 
Ans. 146 lb. 113 33 19 3.375 gr. 
309. Add 33 yd., 47.175 yd., 13.832 yd., 4.09375 yd. 
and 3.116 ft. Ans. 69 yd. 1 ft. 2.067 in. 


SUBTRACTION OF DENOMINATE NUMBERS. 
Art. 176. To subtract denominate decimals ? 


Ruite.—Reduce the given quantities to the same denom- 
ination and subtract as in subtraction of decimals. 


310. From £.625 take £.4875. 
Ans. £.1876 or 3s. 9d. 


311. From £1.25 take 13.5575 shillings. 
Ans. 11s, 5.31d. 


312. From 49.375 lb. take 13.45 dwt. 
Ans. 49 lb. 3 oz. 16 dwt. 13.2 gr. 


142 DECIMAL FRACTIONS, 


313. From .387122 T. take 3 ewt. 1 qr. 15.32 Ib. 
Ans. 4 ewt. 0 qr. 2.12 Ib. 


314, From 15.375 lb. take 11.3875 2. 
Ans. 14 1b,53 13. 
315. From 3 yd. 3 qr. take 1 qr. 2 na. 1.25 in. 
Ans..3 yd. 1 gr.dipa. 1 an. 
816. From 41.24 degrees take 41 m. 38.25 fur. 
Ans. 40 deg. 44 m. 6 fur. 7.6 rd. 
317. From 45 square miles, subtract 14 sq. m. 
551.125 acres. Ans. 30 sq. m. 88 A. 3 R. 20 sq. p. 
318. From 15.331 cords, take 114} cu. ft. 
Ans. 14 cord 56 cu. ft. 59.904 cu. in. 
319. From 15 bbl. 3.25 gal., take 41.865 gallons. 
Ans. 14 bbl. 24 gal. 3.54 qt. 
320. 115.8355 bu., take 3.451 pk. 
Ans. 114 bu. 1 pk. 7.128 qt. 
321. From .3120 of a year of 8651 days, take 29 days 
13.425 hr. Ans. 84 da. 9 hr. 34 min. 1.2 sec. 
322. From 17.09375 A., take 14 A. 3 R. 18.65 sq. p. 
Ans. 2 A. 0 R. 36sq. p. 10.5875 sq. yd. 


MULTIPLICATION OF DENOMINATE NUMBERS. 


Art. 177. To multiply denominate numbers by a 
decimal fraction, 


Ruite.—Reduce the given denominate number to the 
decimal of the highest denomination, and multiply it by 
the multiplier. Or, 

Reduce the multiplier toa vulgar fraction ; divide the 
given denominate number by the denominator, and mulls 
ply the quotient by the numerator. 


323. Multiply £13 10s. by 5. 
Ans, £6.75 or, £6 15s. 


MULTIPLICATION OF DENOMINATE NUMBERS. 143 


324. Multiply £38 15s. 9d. by .15. 
Ans, £5 16s. 4,5. 


325. Multiply 14 Ib. 30z. 11 dwt. 15 gr. by.13 
Ans. 1 Ib. 10 oz. 6 dwt. 2.67 gr. 


326. What is .25 of 50 T. 15 cwt. 3 qr. 15 Ib. ? 
Ans. 12 T. 13 ewt. 3 qr. 22.5 Ib. 


327, What is .47 of 15 1lb.33 43 153? 
Ans. 7]b. 23 23 05D Ter. 


328. What is .10 of 4 E. Fr. 1 qr. 3 na. 1.25 in. ? 
~ Ans, 2 qr. 2 na: 0.8 in, 


329. Multiply 73 m. 4 fur. 32 rd. by 1.25. 
Ans, 91.m. 7 fur. 4.6875 rd, 


330. Multiply 14 A. 3 R. 25 sq. p. by .09. 
| Ans. 1 A. 1 R. 14 sq. p. 19.6625 sq. yd. 


331. Multiply 41 gal. 1 qt. 1.75, pt. by .125. 
Ans. 5 gal. 0 qt. 1 pt. 1.875 gi. 


Notr.—Reduce the following sums to the decimal of that denomination of 
which the value of a unit is given. 


332. What cost 3 cwt. 2 qr. of sugar at $11.25 per 


ewt. ? Ans. $39.37}. 
333. What will 15 T. 15 cwt. 35]b. of-iron cost at 
$56.25 per ton ? Ans. $886.92. 
334. If a bushel of oats cost $.78, what will 59 bu. 3 
pk. 5. qt. cost ? Ans. $46.73. 
335. If a man can earn £2 13s, 4d. in one day, how 
much can he earn in 3.5 days ? Ans. £9 6s. 8d. 
- 336. If an acre cost $175.25, what will 71 A. 3R 
2.5 sq. p. cost ? Ans. $12576.92. 
337. What will be the price 12 T. 13 ewt. 1 qr. 10.5 
lb. of sugar at $12.50 per cwt.? Ans. $3166.94. 


388. What will be the cost of 71 yd. 3 qr. 3 na. of 
cloth, at $5.871 per yard ? Ans, $422.68. 


144 DECIMAL FRACTIONS. 


339. What will 14 ewt. 3 qr. 16 lb. of iron cost, at 


$73.16 a ton 2 Ans, $54.54. 
340. What will 9 oz. 13 dwt. 8 gr. of gold cost, at 
$212.38 a pound ? Ans. $171.08. 
341. If one acre of land cost £37.15s., what will 15 A. 
1 R. 10 sq. p. cost ? Ans. £578 Os. 114d. 


342. If a ton of copper cost £63 17s. 3d., what will 
7 T. 13 ewt. 3 qr. 16 lb. cost? Ans. £491 9s. 03d. 


DIVISION OF DENOMINATE NUMBERS. 


Art. 178, To divide a mixed denominate number 
by a decimal fraction, 


Ruir.—Reduce the given denominate number to the deci- 
mal of the highest denomination and divide it by the 
divisor. Or, 

Divide the given denominate number by the divisor, 
considered as a whole number, and multiply the quotient by 
the number that expresses the order of the decimal. 


343. Divide £591 15s. 9d. by 1.5. 
Ans. £394 10s. 6d. 
344, Divide £5 19s. 112d. by.25. 
Ans. £23, 19s. 11d. 
345. Divide 171 Ib.3 oz. 15 dwt. 21 gr. by 8. 15. 
Ans, 54 Ib, 4 oz, 12 dwt. 1537 or, 
346, Divide 3 ewt. 1 gr. 15 lb. 12 oz. 9 dr. ne “81. 
Ans. 3 ¢wt.8 ar. 14 Ib. ‘7 oz. 8 dr. 
347. Divide 501 lb. 3% 53 15 16 gr. by 17.05. 
Ans, 29 lb. 4.5 65 15 17 gr. 
348. Divide 71 E.E. 3 qr. 1 na. 1 in. by 6.25. 
Ans,. 11 E.E. 2 qr. 1 na..079 in. 


349. Divide 34 deg. 29 m. 3 fur. 21 rd. by .05. 
Ans. 688 deg. 32 m. 6 fur. 20 rd, 


DIVISION OF DENOMINATE NUMBERS. 145 


350. Divide 61 sq. m. 548 A. 1 R. 20 sq. p. by .814. 
Ans. 197 sq. m. 586 A. 3. R. 8 sq. p. 


351. Divide 59 cu. yd. 14 cu. ft. 1500 cu. in. by .75. 
Ans. 79 cu. yd. 10 cu. ft, 1424 cu. in. 
352, Divide 13 hhd. 51 gal. 1 qt. 1.75 gi. by 3.75. 
Ans. 8 hhd. 43 gal. 2.6 gi. 
353. Divide 1 bu. 8 pk. 4.5 qt. by .025. 
. Ans. 75 bu. 2 pk. 4 qt. 


When the number of articles and their value are known, how 
ean the value of a single article be found? (Art. 53.) 


When the value of a single article and the value of several art_- 
cles are known, how can the number of articles be found? (Art 
54.) 


Notr.—The divisor and dividend must be of the same denomination, ex- 
cept when the value of a single article is to be found. 


354. If 3.1 gallons of molasses cost $.93, what will 
one gallon cost ? Ans. $.30. 

355. If'7.5 bushels of rye cost $1.98, what will one 
bushel cost ? Ans, $.264. 

356. If 4.9 lb. of tea cost £1. 18s. 9.5d., what will one 
pound cost ? Ans. 7s. 11d, 


. 357, If 13 ewt. 3 qr. 15 Ib. of sugar be put in parcels 
of 12.5 lb. each, how many parcels will there be ? 
Ans. 111.2 parcels. 


358. If 17.5 acres of land cost £4861. 14s. 44d, what 


will one acre cost? Ans, £27 Teloseod, 
359. If 3 yd. 1 qr. cost $14.75, what will one yard 
cost 2 Ans, $4.5883-+. 


360. If you can buy 15 cwt. 2 qr. 14 lb. of tobacco 
for $100, how much will one hundred weight cost? 
Ans. $6.38938-+. 


361. If a person travels 21.4 miles in 11 hr. 10 m. 30 
sec., how long will it take hin: to travel one mile ? 
Ans. .52219 hr., or 31 min. 20 sec, 
13 


146 DECIMAL FRACTIONS. 


62. If 33 gal. 2 qt. 1.5 pt. cost $124.25, what will 
one ens cost ? Ans. B5, 688-++-. 


363. If 14 bu. 1 pk. 7 qt. cost $18.50, how many 
bushels may be bought for $1 ? 
Ans. .78209 bu.+-or 5 pk. 1 qt. 


364. Ifa yard of silk cost 17s. 43d., how many yards 
can be bought for £251. 15s. 6d.?2 Ans. 289 442 yd. 


365. If a barrel of flour cost $5.50, how many barrels 
can be bought for £79. 4s., New York currency ? 
Ans, 36 barrels. 


366. If you can buy 3 yd. 1 qr. of silk for £1, how 
much will 235 yd. 8 qr. 1 na. cost? £72. 11s. 1d.+. 


367. If 5 bu. 1 qt. cost one dollar, how much will 654 
bushels cost ? Ans. $129.98-+. 


368. If a bottle contain 1 pt. 3.875 gills, how many 
bottles must be used to put up 2 tuns of wine? 
Ans. 2048 bottles. 
369. If 14 yd. 3 qr. 3 na. cost $57.3825, what will one 
yard cost ? Ans. $3.8377 --. 


370. If a person can travel 169 m. 3 fur. 24 p. in 
8.125, days, how far can he travel in one day ? 
Ans, 20.8554 m., or 20 m. 6 fur. 33.728 rd. 


PROMISCUOUS EXAMPLES—DENOMINATE NUMBERS. 
371. If 8.25 yards of silk cost £3. 5s. 6d., what will 


be the price of one yard ? Ans. 78s. 114d.+ 
3872. How much will 61 gal. 2 qt. 1 pt. of oil cost, 
eee 5.5 gal. cost $4.375 ? Ans. $77.03125. 


378. If 2 oz. 10 dwt. of gold cost $35.80, how much 
ee be bought for $260.70 ? 
Ans, 1 Ib., 6 0z., 4 dwt., 24 grs. 
374, How many yards of muslin may be bought for 
£11. 53., when 64.125 yd. cost £8.15625 2 
Ans. 88.4448 yd.+ 


PROMISCUOUS EXAMPES——DENOMINATE NUMBERS. 147 


375. If 18 A. 3 R. 30 sq. p. cost $4545, what will 
150 acres cost ? Ans. $86 000. 


876. If 25.15 yards cost £12. 11s. 9d., what will 5 yd. 

20st ? Ans. £2. 10s. 03d. 
377. If 3 tb. 7 oz. 10 dwt. of silver cost £2. 17s. 9d., 

what will 2.834 Ib. cost? . Ans. £1. 17s. 245d. 


378. If £4. 17s. 6d. be the price of 100 lb. of cheese, 
how many pounds can be bought for £653. 
Ans, 1841.025 Ib. 


379. If 3 ewt. 2 qr. 15.25 lb. of sugar cost $23.50, 


what will 40 pounds cost ? | Ans, $2.5736. 
380. If 162 pounds of mace cost $48.875, what will 
17 ewt. 1 qr. 20 Ib. cost? Ans. $5064.864. 
381. If 334 bushels of peaches cost £1. 10s. 7d., what 
will 180.4 bushels cost ? Ans, £8. 5s. 6.204d. 
382. If 1 +hd. 15.75 gallons of wine cost $150.50, 
what will 112 gallons cost ? Ans, $21.2845-+., 
383. If 4.5 acres cost $2400, what will 94 A. 3 R. 24 
sq. p. cost } Ans. $50613.334 


384. If it cost 2s. 94d. to cart a load of wood 1.125 
miles, how much will it cost to cart 40 cords,7 m. 7 fur., 
allowing 2.275 loads toa cord? Ans. £88. 18s. 34d. 

385. If 1.5 bushels of wheat cost $1.68%, what will 
154 bu. 1 pk. 6 qt. cost ? Ans. $178.74. 

386. If .98 of a yard of cloth cost $5.53, what va 
7 pieces, each piece 37 yd. 2 qr. 1 na., cost ? 

. Ans. $1483.71875. 


387. If 2.6 gallons of wine cost £2. 17s. 9d., what 


will 43 gal. 2 qt. cost 2 Ans. £48 6s. 214d. 
388. Ifa 1.45 hhd. of brandy cost £44. 13s. 4d., what 
will 5 hhd. 15.75 gal. cost?  ‘ Ans. £161. 4s. Add, 


389. If A can do a piece of work in 2.5 days, and B 
can do it in 3 days, how long would it take them both 
together ? Ans. 1,4. 


148 PERCENTAGE. 


390. If A can mow 12 acres of wheat in 12.5 days, 
and B in 13.5 days, how long -will it take the two togeth- 


5] : 
er? Ans. 65 days. 


391. If A and B together can consume a barrel of pro- 
visions in 16.5 days, and A can do it alone in 27.5 days, 
how long will it last B alone ? Ans. 41.25 days, 


PERCENTAGE, 
Art. 179. What is Percentage ? 
Percentage is a certain rate on one hundred. 


Art. 180, How is percentage written ? 


By hundreds in the form of a decimal. Thus, 


1 per cent. is written .01 
+ 66 ce 66 6b 02 
7 14 6c 66 6c .07 

10 66 66 66 66 .10 


Crom] Bop 
o = e e 

=) 

Sh 
e) 

ter: 
> 
S 
ee) 
he 
|r 


Hee ee ee ea PN | 


Art. 181. To find the per cent. of any number, 
Rutz.—Multiply the given number by tie rate per cent. 


PERCENTAGE. 149 


1. What is 1 per cent. of $100 ? Ans. $1. 


2. What is 1 per cent. of 250 bushels ? 
Ans. 22 bu. 


3. What is 1 per cent. of $36.50 ? Ans. .365, 


4, What is 1 per cent. of $1936 yd. ? 
Ans, 19.36 yd. 


5. What is 10 per cent. of $750. Ars. $75. 


6. What is 10 per cent of 694 Ib. of sugar ? 
Ans, 69.4 Ib. 


7. What is 10 per cent. of $19.25. Ans. $1.924. 


8. What is 20 per cent. of $329.621? 
Ans. $65.922. 


9. What is 12 per cent. of 20 pounds of gold, valued 
at $17.70 per ounce ? Ans, $509.76. 


10. What is 15 per cent. of 964 eggs? 
Ans. 144.6 eggs. 


11. What is 35 per cent. of $10000 ? 
Ans. $3500. 


12. What is '76 per cent. of 2654 bushels ? 
Ans. 2017 bu. 0 pk. 1.28 qt. 


13. What is 100 per cent. of $5. Ans. $5. 
14. What is 332 per cent. of $660? Ans. $220, 


15. What is 123 per cent. of 900 gal. ? 
Ans. 1124 gal. 
16. What is 25 per cent. of $1841.25? 
Ans. $460.313, 
17, What is 374 per cent. of £2971 ? 
Ans, £1114, 2s. 6d. 


18. What is 50 per cent. of 75 hhd. ? 
Ans. 37 hhd. 81 gal. 2 qt. 


19, What is 75 per cent. of 41 sq. rods? 
Ans. 30 sq. rd. a ae yd. 6 sq. ft. 27 sq. in. 


150 ; PERCENTAGE. 


20. What is 162 per cent. of 52 tons ? 
Ans, 8 T. 13 cwt. 14 qr. 


21.. What is 18 per cent. of 71 lb. 6 oz. 6 dwt? 
Ans. 12 lb. 10 0z. 9.88 dwt. 


22. What is 7 per cent. of 153 yd. 3 qr. 
Ans. 10 yd. 3.05 qr. 


23. What is 17 per cent. of 7 m. 3 fur. 20 p.? 
Ans. 1 m. 2 fur, 4 p. 3.3 yd. 


24, What is 5 per cent. of 8361 A. 2 R. 17 sq. p. ? 
Ans. 18 A. 0 R. 12.85 sq. p. 


25. What is 1 per cent. of 15 hhd. 30 gal. 3 qt. 1 pt.? 
Ans. 9 gal. 3 qt. .07 pt. 


26. What i is 2 per cent. of 725 bu. 3 qt. ? 
Ans, 14 bu. 2 pk. .06 qt. 


27. What is 100 per cent. of 3 yd. 2 qr. 1 na. ? 
| Ans. 3 yd. 2 qr. 1 na. 


28. What is 125 ber cent. of $4725 ? 
Ans. $5906.25. 


29, What is 186 per cent. of 16 cwt. 3 qr. 11 lb? 
Ans. 31 cewt. 1 qr. 10.96 Ib. 


30. What is 200 per cent. of $6252 Ans. $1250. 


31. What is 250 per cent. of £713 15s. ? 
Ans. £1784 7s. 6d. 


82, What is 247 per cent. of £116 2 
Ans. £286 10s. 4.8d. 


33. What is 82 per cent. of $16202 Ans. $135. , 


34, What is } pet cent. of 1000 eggs ? 
Ans, 5 eggs 


35. pibas is # per cent. of $1299.332 ? 
Ans. $9.745, 


36. oteet# is £ per cent. of £1905 10s. ? 
Ans. £16 138s, 5.55d. 


37. What is 2 per cent. of $11.43? Ans, $.0762. 


PERCENTAGE. “ot 


38. What is 75 per cent. of £126 1s. 6d. ? 
Ans. 2s. 61d. 
39. A person had $750, and lost 123 per cent. of it; 


how much did he lose ? Ans, $93.75. 
40. A field contains 189 acres; 33} per cent. of it 
was sold; how much was left ? Ans, 126 acres. 


41. A general had an army of 5408 men; he lost 64 
per cent of them in an engagement; how many men did 
he lose ? Ans, 338. 


42, A merchant bought 15 pieces of broadcloth, each 
piece containing 514 yards; on examination 50 per cent. 
proved to be damaged; how many yards of good cloth 
were there ? Ans. 2342 yd. 


43. A person invested $3360 in a speculation, and 
made 662 per cent., how much money did he then have ? 
Ans. $5600. 
44, A man bought a house for $1225.50; in the 
course of 2 years it increased in value 147 per cent. ; 
how much was the house then worth ? 


Ans. $3026.985. 


45. A lady had $76.20; she spent 74 per cent. of it 
in dry goods ; how much did she have left? 
Ans. $70.485. 


46, A person has a bill of $350 against another; he 
consents to deduct } per cent. for cash; how much does 
he receive ? Ans. $349.561. 


47. A person had $5420; he purchased goods with 
371 per cent. of it, 25 per cent. of the balance he lent 
to a friend; how much did he have left ? 

Ans, $2540.625. 


Art. 182. To find what per cent. one number or 
quantity is of another of the same name or kind, 


Ruize.—Place the given number or quantity in the 
numerator and the one with which it rs to be compared, in 


152 PERCENTAGE. 


the denominator ; reduce both terms to the same denomi- 
nation and then to a decimal ; the first two figures to the 
right of the point will be the per cent. required. 


48, What per cent. is 1 of 4? Ans. .25, 
49, What per cent. is 1 of 5? Ans, .20, 
50. What per cent. is 2 of 10? Ans. .20. 
51. What per cent. is 3 of 50? Ans. .06. 
52. What per cent. is 7 of 16? Ans. .433, 
53. What per cent. is 3 of 1? Ans. .75. 
54. What per cent. is 2 of 25? Ans. .013. 
55. What per cent. is 3 of 100? Ans. .003. 
56. What per cent. is 7% of 623? Ans. .0142. 
57. What per cent is 3.5 of 35 ? Ans. .10. 


58. What per cent. is 7.5 of 15% Ans. 50 pr. ct. 
59. What per cent. is 300 of 60? } 
Ans. 500 pr. ct. 
60. What per cent. is 250 of 64? 
Ans. 3.902 pr. ct. 
61. What per cent. is 2s. 8d. of £1 ? 
Ans. 134 pr. ct. 
62. What per cent. is 15s. 9d. of £1 ? 
Ans. 782 pr. ct. 
63. What per cent. is 3 fur. 20 rd. of one mile ? 
Ans, 433 pr. ct. 
64, What per cent. is 5 fur. 16 rd, 23 yd. of one mil 
Po Ans. 6724 pr. ct. 
65. What per cent. of $25 is $3.50 ? 
Ans. 14 pr. ct. 
66. What per cent. of one square mile is 154 A. 3 R. 
15 sq. p. # Ans. 247199; pr. ct. 
67, What per cent. of 172 is 342? 


? 


£4) 


Ans. 20 pr. ct. 


COMMISSION. 153 


68. What per cent. of 16 is 2 of 1234 2? 
Ans. 5152 pr. ct. 


69. What per cent. of 18.25 is 3.375 ? 
Ans. 183$ pr. ct. 


_ 70. What per cent. of 40 is .0125 ? 
Ans. .0003125 or s1, pr. ct. 


COMMISSION. 


Arr. 183. What is Commission 2 


Commission is an allowance made to one person for bug 
tng or selling goods for another. 


Art. 184, How is commission calculated ? 
By a percentage. 
Art. 185. To find the commission, 


Route.— Multiply the given sum by the rate per cent. ; 
the product will be the commission. 


1. A commission merchant sold 500 pieces of bomba- 
zine for $30 a piece; what was his commission at 2 per 


cent. ? Ans. $300. 
2. An auctioneer sold a house for $3125; what was 
his commission at 1 per cent. ? Ans. 31.25. 


3. A merchant sold on commission, 300 barrels of 
flour at $7 a barrel; what was his commission at 24 per 
cent. ? Ans. $52.50. 


* 4, Sold at auction 30 hogsheads of tobacco, at $105 a 

hogshead; what were the auctioneer’s fees at 34 per 

cent. ? Ans, $102,374. 
5. Sold at auction a house for $6500 and the furniture © 


for $5650; what were the auctioneer’s fees at 24 per 
cent. ? — Ans. $258.18. 


154 COMMISSION. 


6. A cominission merchant sold 12 pieces of muslin, 
each piece 304 yar ds, at 11 cents a yard; what was the 
commission at 54 per cent. ? | Ans, $2.20. 


7. Sold 42 tons, 18 ewt. 38 Ib. of iron at 14 cents a 
pound ; what is the commission at 32 per cent. ? 
Ans. $40.23+. 


8. A butter dealer received 75 firkins of butter, each 
firkin 56 lb., to sell on commission ; he sold them at 223 
cents a pound ; what was his commission at 10 per cent., 
and what did he return to the owner 2 

i ei $94.50 commission, 
$850.50 returned. 


9. Sold at auction, 150 hogshead of sugar, each hogs- 
head weighing 11 cwt. 50 Ib., at $7 25, hundred ; what 
was the “auctioneer? S commission at 14 per cent., and 
to how much was the owner entitled ? 

Wee 1 $150.93% commission, 
~* 1 $11924.064 for owner. 


Arr. 186, To find the commission when the commis: 
sion and purchase are both to come out of the same sum, 


Rute.— Divide the given amount by 1, inereased by the 
per cent. ; the quotient will be the amount of the pur. 
chase, and the balance of the money will be the commis- 
sion. 


10. A commission merchant received $10000 to be 
invested in cigars; what was the commission at 5 per 
cent., and how much was he to expend ? 

ae $9523.81 expended, 
" 1 $476.19 commission. 

A real estate. broker received $100000 to be in 
vested in property, after deducting his commission at 7 
ver cent.; what was his commission, and how much did 
he invest in property ? 1 $6542.06 commission, 

’ | $93457.94 in property. 

12. An agent received $8500, to buy cotton for a fac. 


INSURANCE. 155 


tory, after deducting commission at 1? per cent.; he 
bought at 8 cents a pound. How many pounds did he 
buy ? Ans. 429973 Ib. 


13. A real estate agent purchased a house and charged 
2} per cent. for services rendered; he sent in a bill of 
$3224.24 ; what did he pay for the house ? 

Ans. $3145.60. 

14. A merchant in London sent to his agent in New 
York £7786. 4s. 10d. to be invested in flour, after de- 
ducting 4 per cent. commission on the sum to be expend- 


ed, what was the amount of his commission ? 
Ans, £299, 9s. 5d. 


INSURANCE. 


Art. 187. What is Insurance 2 


Insurance is the payment of a certain sum of money in 
order to secure the value of property destroyed or injured 
by fire, water, or other accidents. 


Art. 188. How is insurance calculated 2 


By percentage. 


1. What will it cost to insure the stock of a store, 
valued at $18500, at 14 per cent. ? Ans, $168.75, 


2. What does it cost to insure a vessel worth $800 at 
21 per cent. ? Ans. $17. 


3. What does it cost to insure a store ee th $6850, 
at 4 per cent., and the stock $7683.45 at 3 per cent. ? 
: Frist £63. O06, 


4, What does it cost to insurea vessel worth $13000, 
at 24 per cent., and the cargo $18268.50, at 12 per 
cent. 2 Ans. $618. ag. 


156 INSURANCE. 


5. A piano maker has 25 pianos worth $375 each; 
what will it cost to obtain insurance upon them at 50 
cents on a hundred dollars ? Ans. $46.88. 


6. What will a person have to pay to get furniture 


worth $3500 insured, at 35 cents on $1002 
Ans. $12.25, 


7. What does it cost to insure } of a vessel worth 
$27500, at 32 per cent., and 2 of the cargo worth 
$126875, at 2 per cent. ? Ans. $2223.75. 

8. A person bought a house, and paid the insurance 
at 2 per cent.; the whole of which amounted to $2040 ; 
what was the value of the house, and how much was the 
the insurance ? 

Pte | $4 $2000 for the housa, 
* (840 “ “ insurance. 


9. A cotton broker bought and insured at 31 per 
cent., 50 bales of cotton; he paid for the whole 89750; 
what was the price per bale of the cotton, and how much 


the insurance 2 
$53.14 per bale, 


$93 for insurance, 


Ans. 


10. A factory worth $17550, was insured at 10 per 
cent. for such an amount as would cover the value of the 
building and the insurance; what was the amount 
insured 2 Ans. $19500. 

11. A merchant shipped 400 barrels of fish at $3.50 
per barrel; for what amount must he insure at 5 per 


cent., to cover the value of the fish and insurance 2 
Ans. $1478.68. 


12. If it costs $400. to get a vessel worth $1250 
insured, what is the percentage? Ans. 3} per cent. 
13. I have a stock of goods worth $37560.75 ; I get 
4 insured for $178.20; what is the rate per cent. ” 
Ans. $.593 on $100. 
14. A merchant imported 3865 pieces of silk, each 
piece 444 yards, at $2.40 a yard; he got them insured 


pROKERAGE AND STOCKS. 157 


at 54 per cent. on the selling price of $3 a yard; if fire 
should destroy those goods, and he get the amount 
-insured for, how much would he make? 

Ans. $7065.49. 


15. A merchant imported 450 pieces of silk, each 
piece 351 yd., at $1 a yard; what was the insurance at 
42 per cent. ? Ans, $713.81. 


16. Shipped from Havre to New York, $40000 worth 
of merchandise; it was divided into 20 equal portions, 
and sent in as many different vessels without insurance ; 
if one shipment be lost, would it be more or less advan- 
tageous, than making one shipment of the whole, receiv- 
ing the goods safely, and paying insurance at 6 per 
vent. ? Ans. $400 gain. 

17. A cotton broker sent 500 bales of cotton to 
Liverpool; each bale weighed 950 Ib., and the cost was 
111 cts. a pound; the whole was insured for $2185; 
what was the per cent. ? Ans, 4 per cent. 

18. Shipped from New York to London 10000 
bushels of corn, 311 cts. a bushel; the whole was 


insured for $234.374 ; what was the per cent. ? 
Ans. 72 per cent. 


BiVOQiGE RA GEA N DAS TOG ISS: 


Art. 189. What is Brokerage ? 


Brokerage is an amount of money paid to a person 
cailed a broker, for dealing in money, stocks, de. 


Art. 190. What is stock ? 


Stock is the capital of an individual or company, and 
consists of money, goods, &c. 


Arr. 191. How is stock divided ? | 
Into parts called shares, usually of $100 each. 
; 14 


158 BROKERAGE AND STOCKS. 


Art. 192 When is stock said to be at par? 


When a share is worth the amount for which it was 
first issued, 


Art. 193. When is stock above par ? 


When it is worth more than the amount for which u 
was first issued, 


Art. 194, When is stock below par ? 


When it ts worth less than the amount for which it was 
Jirst issued, 


Art. 195. How is the amount of the rise and fall of 
stock estimated 2 


By percentage. 


1. What is the value of 10 shares of Erie Railroad 
stock, at $85 a share ? Ans. $850. 
2. What is the value of 16 shares, par value $100, 
of Union Bank stock, at an advance of 12 per cent. ? 
Ans. $1792. 
3. What is the value of 80 shares, par value $100, of 
Hudson River Railroad stock at 17 per cent. below par? 
Ans. $2490. 
4, What is the value of 25 shares of New Haven 
Railroad stotk at 18 per cent. advance, the par value be- 
ing $100 a share } Ans. $2950. 
5. What is the value of 48 shares of Bank stock at 53 
per cent. advance, par value $100 a share ? 
Ans. $5064. 
6. A broker purchased 86 shares of Crystal Palace 
stock at $43 a share; what is his brokerage at 14 per 
cent., par value $100 ? Ans. $19.35. 


7. What is the brokerage at 12 per cent., for purchas 


BROKERAGE AND STOCKS. 159 


ing 50 shares of the New York Gas Co. stock, at 45 per 
cent. advance, par value $100 a share. 
Ans. $99.69. 


8. What will a broker charge to change $450 uncur- 
rent into current money, at 1 per cent. discount ? 
Ans. $4.50. 


9 What will a broker charge’to change into current 
money $3654 of the bills of the Bank of Ohio, upon 
which there is a discount of 21 per cent. ? 


Ans, $82.22. 


10. A person has $3000 of the Bank of Indiana, upon 
which there is a discount of 34 per cent., and $2000 of the 
Bank of Pennsylvania, upon which there is a discount of 
14 per cent. ; how much will a broker charge to change 
the amount into current money ? Ans. $130. 


11. A person lad $5500 in uncurrent money which he 
wanted to change into current; upon $500 of the above 
there was a discount of 2 per cent., on $650, 24 per cent., 
on $325, 14 per cent., on $1000, 14 per cent., on $2250 
4 per cent., and on the remainder, 1 per cent. ; what will 
he charge to discount the whole ? Ans. $61. 


12. What will a person receive for $250 uncurrent 
money upon which there is a discount of 24 percent. ? 
Ans. $243.90. 


13. A person has $3200 in bills of the Bank of Mary- 
Jand on which there is a discount cf 32 per cent. ; what 
will he receive in bankable money if the brokerage be 
taken out of the above amount ? Ans. $3080. 


14, A person has $350 upon which there is a discount 
of 14 per cent.; $725, 24 per cent. discount; $1236, 2 
per cent. discount, and $300, 1 per cent. discount ; what 
will he receive if the brokerage be taken out of the 
money changed ? Aus, $2563.932. 


@ 


160 INTEREST. 


INTEREST. 


Art. 19§. What is Interest 2 


Interest is a rule for calculating what should be paid 
for the use of money. 


Art. 197. What are the terms used in interest? 
Principal, Interest, Amount, Rate per cent., and Time. 
Art. 198. What is the principal ? 

The Principal is the sum of money at interest. 

Arr. 199. What is the interest ? 

Interest is the sum paid for the use of the a 
Art. 200. What is the amount ? 


The amount is the sum of the principal and interest, 
NotTE.—Per Annum, signifies “‘ by the year.” 


Art. 201. To find the interest of any sum of money 
for one year, 


Rurz.-—Multiply the given sum by the per cent. per an 
Num. 


1. What is the interest of $712 for one year, at 6 per 


cent. per annum ? Ans. $42.72. 

2. What is the interest of $329.50 for one year, at 7 
per cent. per annum ? Ans. $23.065. 

3. What is the interest of $986.30 for one year, at 64 
per cent. per annum ? Ans. $64.109+. 

4, What is the interest of $12600 for one year at 43 
per cent. per annum ? Ans. $554.40. 


5. What is,the amount of $14 for one year, at 34 per 
cent. per annum ? Ans, 14.49, 


INTEREST, 161 


6. What is the amount of $4186.25 for uo. —; sar, at 
54 per cent. per annum ? Ans. $4416.498. 


7. What is the amount of £168 for one year, at 7 per 
cent. per annum ? Ans. £179. 155,°2d. 12. q. 

8. What is the interest of £286. 12s. for one year, at 
Sy per cent. per annum ? Ans. £24. Ts. 24d. 


9. What is the amount of £3856. 18s. 9d. for one 
year, at 5 per cent. per annum ? 
Ans. £4049. 15s. 81d. 


10. What is the interest of $1745.40 for one year at 


162 per cent. per annum ? Ans. $290.90. 
11. What is the amount of $1001.75 for one year, at 
62 per cent, per annum } Ans. $1068.15.+. 


12. What is the amount of £44 3s. 103d. for one 
year, at 54 per cent. per annum? Ans. £46 11s.+ 
13. What is the amount of £75 13s. 5d. for one year, 
at 62 per cent. per annum? Ans. £80 15s. 62d.+ 
"14. What is the amount of $800.07 for one year, at 
7% per cent. per annum ? Ans. $862.075. 
15. What is the amount of $1601.51 for one year, 
at 81 per cent. per annum ? Ans. $1733.634+. 
16. What is the amount of $7266.28 for one year, at 
104 per cent. per annum ? Ans. $8011.073. 


Art. 202. To fmd the interest for two or more years, 


Rute.—Find the interest for one year and multiply it 
by the number of years. 


17. What is the interest of $450 for 2 years at 6 per 
cent. per annum ? Ans. $54.00. 
18. What is the interest of $700 for 3 years, at 7} per 
cent. per annum ? Ans. $157.50. 
19. What is the interest of $3875.20 for 5 years, at 43 
per cent. per annum ? Ans. $920.36. 
14* 


162 INTEREST. 


20, What is the interest of £2000 for 7 years, at 84 
per cent. per annum ? Ans. £1166 13s. 4d. 


21. What is the interest of £1655 13s. 8d. for 6 years, 
at 42 per cent. per annum? Ans, £484 5s. 83d.+ 


22. What is the amount of $7500 for 5 years, at 3} 


per cent. per annum ? Ans. $8718.75. 
23. What is the amount of $11459.621 for 3 years, at 
102 per cent. per annum ? Ans. $15069.406 +. 


24, What is the amount of £1215 5s. 2d. for 2 years, 
at 54 per cent. per annum ? 
Ans. £1348 18s. 83d. 
25. What is the amount of £1 for 11 years, at 43 per 
cent. per annum ? Ans. £1 10s. 2d. 
26. What is the amout of $1 for 5 years 33 per cent. 
per annum ? Ans. $1.18. 
27. What is the interest of £144 2s. 81d. for 8 years, 
at 61 per cent. per annum ? Ans. £72 1s. 43d. 
28. What is the interest of $500 from June Ist, 1837, 


to June Ast, 1840, at 61 per cent. per annum ? 
Ans. $97.50. 


29. What is the interest of $1694.20 from Jan. 4th, 
1845, to Jan. 4th, 1849, at 51 per cent. per annum ? 
Ans, $355.782. 


30. What is the amount of $2175.68, from July 15th, 
1841, to July 15th, 1846, at 74 per cent. per annum ? 
Ans. $2991.56. 


Arr. 203. To find the interest for years and months, 


Rute.—Lind the interest for one year and divide it by 
12 to obtain the interest for one month ; then multiply the 
interest for one year by the number of years, for one month 
by the number of months, and udd the two products. Or, 


Multiply the given sum by the product of the percentage 
and time, expressed in years or fraction of a year. 


INTEREST. 163 


31. What is the amount of $1 for 2 yr. 6 mo. at 8 


per cent. per annum ? Ans. $1.20. 
32. What is the amount of £1 for 3 yrs. 4 mo. at 53 
per cent. per annum ? | Ans. £1 3s. 8d. 
33. What is the interest of $68.75 for 2 yr. 2 mo. at 
4} per cent. per annum ? Ans. $6.708. 
34, What is the interest of $400.60 for 3 yr. 9 mo., at 
Di per cent. per annum ? Ans. $82.623. 


35. What is the interest of £284 10s. 6d. for 3 yr. 5 
mo. at 7 per cent. per annum? Ans. £68 Os. 113d. 


36. What is the amount of $911.124 for 2 yr. 8 mo., 


at 3% per cent. per annum ? Ans. $993.126+. 
37. What is the interest of $1980.44 for 8 mo., at 
4% per cent. per annum ? Ans. $62.713-+. 
38. What is the’amount of $1000 for 9 mo., at 5} 
per cent. per annum ? Ans. $1039.375. 
39. What is the amount of $100 for 10 mo., at 74 
per cent. per annum ? Ans. $106.25. 
40. What is the interest of $10 for 19 mo., at 7 per 
cent. per annum ?. Ans. $1.108. 


41. What is the interest of $1250.53 for 2 yr. 11 
mo., at 3+ per cent. per annum? Ans, $113.98+. 

42. What is the interest of £88 10s. for 6 mo., at 6 
per cent. per annum ? Ans. £2 18s. 1d.+ 

43, What is the amount of £145 12s. 6d. for one yr. 


10 mo., at 81 per cent. per annum? 
Ans. £168 6s, 43d. 


44, What is the amount of £2500 for 3 yr. 11 mo., at 
41 per cent. per annum ? Ans. £2916 2s. 11d. 


* 45. What is the interest of £10000 for 3 yr. 7 mo., 
at 43 per cent. per annum ? Ans. £1567 14s. 2d. 


46. What is the interest of £1000 for 23 mo., at 6% 
per cent. per annum ? Ans. £115, 


164 INTEREST. 


47. What is the interest of 5000 francs for 13 mo., 
at 41 per cent. per annum? Ans. 230.20-+ francs. 


48. What is the amount of $6841.45 for 2 yr. 4 mo., 
at 5 per cent. per annum ? Ans. $7639.619+. 


49. What is the amount of $5010 for 14 mo., at 33 
per cent. per annum ? Ans. $5221.881+. 


50. What is the interest of $722.11 for 13 yr. 4 mo., 
at 74 per cent. per annum? Ans. $722.11. 


51. What is the amount of $2000, from June Ist, 
1827, to Oct. Ist, 1832, at '7 per cent. per annum ? 
Ans. $2746.663-. 
52. What is the amount of $1850, from July Ist, 
1850, to Jan. 1st, 1853, at '7 per cent. per annum ? 
Ans. $2173.75. 
53. What is the amount of $3125.75, from Oct. Ist, 
1837, to Sept. Ist, 1840, at 5 per cent. per annum ? 
Ans. $3581.58. 


54. What is the interest of $13491.50, from March 
Ist, Rest to August Ist, 1852, at 8 per cent. per an- 
num ? _ Ans. $4766.996+. 


5h. What is the interest of $1786.90, from June 
20th, 1845, to July 20th, 1850, at 6 per cent. per an- 
num. Ans. $545.004+. 


56. What is the interest of £520 18s. 6d., from 
Dec. 24th, 1849, to Nov. 24th, 1850, at 4 per cent. 
per annum ? Ans. £19 1s. 92d. 


57. What is the amount of £3106 15s. 8d.,-from 
April 15th, 1851, to Dec. 15th, 18538, at '7 per cent. 
per annum ? Ans. £3686 14s. 33d.+ 


Art. 204. To find the interest for years, months, 
and days, 


_ Find the interest for one year, one month, and one day ; 
multiply the interest for one year by the number of years, 
Sor one month by the number of months, and for one day 


INTEREST. 165 


by the number of days ; the sum of the three products will 
be the interest. Or, 


Multiply the given principal by the product of the per 
cent. and time, expressed in years or the fraction of a year, 


NotTr.—Count 30 days to a month, which gives 360 days toc year ; 360 days 
has been considered as a commercial year on account of the number being di 
visible by so many other numbers, a property which facilitates the finding of 
interest by means of aliquot parts; and this method of calculating interest 
should be trequently employed by the pupil. 

Since tables of interest, forany number of days, are now extensively used, 
based upon 365 days to to the year, it is probable, at least so far as interest for 
days is concerned, that the last number will be the most employed in ins 
terest. 


58. What is the interest of $100 for 1 yr. 8 mo. 10 


days, at 6 per cent. per annum ? Ans. $7.66. 
59. What is the interest of $1000 for 9 mo. 15 days, 
at 7 per cent. per annum ? Ans. $55.4163. 


60. What is the interest of $1'700 for 2 yr. 3 mo. 10 
days, at 5 per cent. per annum ? Ans. $193.611. 


61. What is the interest of $3000 for 25 days, at 7 


per cent. per annum ? Ans. $14.583. 
62. What is the interest of £2500 for 5 mo. 18 days, 
at 44 per cent. per annum ? Ans. £52 10s. 
63. What is the interest of £1 for 2 yr. 11 mo. 19 
days, at 3 per cent. per annum ? Ans. 1s. 9.88. 
64. What is the amount of $1 for 2 yr. 6 mo. 12 
days, at '7 per cent. per annum? Ans. $1.17732. 
65. What is the amount of $1 for 9 mo. 22 days, at 
6% per cent. per annum ? Ans. $1.054. 


66. What is the interest of $450.50 for 3 yr. 5 mo 
20 days, at 5 per cent. perannum? Ans. $78.211-+. 
67. What is the amount of £145 12s. 6d., for 1 yx 
10 mo. 16 days, at 84 per cent. per annum? 
Ans. £168 17s. 44d. 


68. What is the interest of $710.01 for 3 yr. 11 me 
8 days, at 7 per cent. per annum? Ans. $195.765. 


166 INTEREST. 


69. What is the interest of $44'70.80 for 4 yr. 5 mo. 
10 days, at 734 per cent. per annum? Ans. $1490.266. 


70. What is the interest of $2000 for 75 days, at 44 


per cent. per annum ? Ans. $17.71. 
71. What is the amount of $3600 for 53 days, at 54 
per cent. per annum ? Ans. $3629.15. 
72. What is the amount of $25000 for 13 days, at 8 
per cent. per annum ? Ans. $25072.222. 
73. What is the interest of $14.50 for 19 days, at 6 
per cent. per annum ? Ans. $.04594. 
74. What is the amount of $112.75 for 100 days, at 
8} per cent. per annum ? Ans. $115.359+. 


75. What is the interest of $6000 for 11 yr. 1 mo. 
10 days, at 9 per cent. per annum ? Ans. $6000. 

76. What is the amount of £10000 for 8 yr. '7 mo. 
12 days, at 6 per cent. per annum? Ans. £12170. 

77. What is the interest of $7000 for 6 yr. 5 mo. 11 
days, at ‘7 per cent. per annum? Ans. $3159.138. 


78. What is the interest of $400, from March Ist, 
1847, to July 16th, 1849, at 7 per cent. per annum ? 
| Ans. $66.50. 
79. What is the interest of $2311.50, from May 34, 
1850, to January 16th, 1853, at 6 per cent. per annum ? 
: Ans. $374.848+. 
« 80. What is the amount of £980, from October 13th, 
1836, to June Ist, 1840, at 5 per cent. per annum ? 
Ans. £1158 Os. 8d. 


81. What is the amount of £257 13s. 6d., from July 
1st, 1844, to July 17th, 1844, at 64 per cent. per an- 
num ? Ans. £258 8s. 43d.+ 

82. What is the amount of $3155.49, from August 
15th, 1841, to May Ist, 1849, at 6 per cent. per an- 
num ? Ans. $4615.48. 

83. What is the amount of $10, from November 19th, 


¢ 


INTEREST. 167 
1836, to December Ist, 1849, at 54 per cent. per an- 
Auiat? Ans. $17.169. 


Arr. 205. To find the interest of any sum at 6 per 
cent per annum, 


Ru.e.— Consider feat 6 per cent. per annum gives 
per cent. a month, and 35 per cent. a day ; multiply the 
6 per cent. by the umber of years, the 4 per cent. by the 
number of months, and = per cent. by the number of days ; 
add these three pr oducts Wags and their sum will be the 
percentage for the whole time ; multiply the given sum by 
this percentage, and the product will be the interest for the 
given lime. 


Arr. 206. To change the interest at a known rate per 
cent. per annum, into the interest at another rate, per 
cent. per annum, 


Rutz.—Add to, or take from the interest at a known 
rate per cent. per annum such a part of itself as the excess 
or deficiency of the required rate per cent. per annum is of 
the known rate, 


84. Find the interest of $600 for 2 yr. 8 mo., at 6 per 
cent. per annum, and change it to 5 and 7 per cent, per 
annum, at 6 per cent. $96. 

: A at 5 per cent. $80, 
} at 7 per cent. $112. 


85. Find the interest of $450 for 3 yr 7mo., at 6 per 
cent. per annum, and change it to 4 and 8 per cent. per 
annum ? at 6 per cent. $96.75. 

Ans at 4 per cent. $64.50. 
at 8 per cent. $129.00. 


86. Find the interest of $2964.12 for 11 mo., at 6 
per cent. per annum, and change it to 7 and 8 per cent. 
per annum. “| at 6 per cent. $163.026. 

Ans 


4 


at 7 per cent. $190.197. 
at 8 per cent. $217.368, 


168 INTEREST, 


87. Find the interest of $785.10 for 1 yr. 6 mo. 18 
days, at 6 per cent. per annum, and change it to 5 
and 9 per cent. per annum. 

at 6 per cent. $73.014. 
Ans. 4 at 5 per cent. $60.845. 
at 9 per cent. $109,521. 


88. Find the interest of $1420.50 for 2 yr. 3 mo. 25 
duys, at 6 per cent. per annum, and change it to 3, 4, 
and 7} per cent. per annum. 

at 6 per cent. $197.686. 

Ans, J 2% 8 per cent. $98.843. 
") at 4 per cent. $131.79. 
at 71 per cent. $247.107. 


89. Find the interest of $12850, for 90 days, at 6 per 
cent. per annum, and change it to 44, 5, and 7 per cent. 
per annum. at 6 per cent. $192.75. 

| Ans, 2 2¢ 43 per cent. $144.562. 
“| at 5 per cent. $160.625. 
at 7 per cent. $224.875. 


- 90. Find the interest of $750 for 9 mo. 17 days, at 6 
per cent. per annum, and change it to 5 and 7 per cent. 
- per annum. ! at 6 per cent. $35.875. 

Ans, 4 at 5 per cent. $29.895. 
at 7 per cent. $41.854. 


91. Find the interest of $3654.25 for 33 days, at @ 
per cent. per annum, and change it to 10 and 11 per 
cent. per annum. at 6 per cent. $20.098. 

Ans. 4 at 10 per cent. $383.497. 
at 11 per cent. $36.846. 


92. Find the interest of $1411.26, for 123 days, at 6 
per cent. per annum, and change it to 12 and 138 per 
cent per annum. at 6 per cent. $28.93. 
at 12 per cent. $57.861. 
at 13 per cent. $62.683. 


93. Find the terest of $14544.20 for 183 days, at 6 


Ans. 


INTEREST. 169 


per cent. per annum, and change it to 14 and 15 per cent. 

per annum. at 6 per cent. $443.598 

Ans. at 14 per cent. $1035.062 
at 15 per cent. $1108.995 


94, Find the interest of £400 for 7 mo. 11 days, at 6 
per cent. per annum, and change it to 5- and 7 per cent. 
per annum. at 6 per cent. £14 14s. 8d. 
at 5 per cent. £12° 5s. 62. 
at 7 per cent. £17 3s, 92. 


95. Find the interest of £300 for 2 yr. 7 mo., at 6 
per cent. per annum, and change it to 4 and 5 per cent. 
per annum, at 6 percent. £46 10s. 

Ans. | at 4 per cent. £31. 
at 5 per cent. £38 15s. 


96. Find the interest of £601 12s. for 78 days, at 6 
per cent. per annum, and change it to 9 and 10 per cent. 
per annum. { at 6 per cent. £7 16s. 31d. 
Ans. 4 at 9 per cent. £11.14s. 514d. 

lat 10 per cent: £13 0s. 62d, 


97. Find the interest of £71 9s. 103d. for 23 days, at 
6 per cent. per annum, and change it to 12 and 15 per 
cent. per annum. (at 6 per cent. 5s. 53d. 
Ans. at 12 per cent. 10s. 114d." 
at 15 per cent. 13s, 83d. 


98. Find the amount of $1700 for 100 days, at 6 per 
cent. per annum, and change it to the amount at 5 and7 
per cent. per annum. : at 6 per cent. $1728.333. 

ns 


Ans. 


Af 


at 5 per cent. $1723.61. 
at 7 per- cent. $1733.06. 


99. Find the amount of $929.90 for 2 yr. 1 mo., at 6 
per cent. per annum, and change it to the amount at 5} 
and 63 per cent. per annum. 

at 6 per cent. $1046.137. 
Ans. . at 54 per cent. $10386451. 
at 64 per cent. $1055.828. 


100, Find the amount of $16941.20 for 1 yr. 7 mo, 
1d 


170 INTEREST, 


28 days, at 6 per cent. per annum, and change it to the 
amount at 47 and 84 per cent. per_annum. 
at 6 per cent. $18629.672. 
Ans. 4 at 43 per cent. $18277.907. 
7 at 84 per cent. $19286.29. 
101. Find the amount of £3000 for 6 mo. 17 days, at 
6 per cent. per annum, and change it to 124 and 15 per 
cent. per annum. his 6 per cent. £3098. 10s, 
Ans 


at 124 per cent. £5205. 4s. 2d. 
at 15 per cent. £3246. 5s. 
102. Find the interest of $2500 for '7 mo. 20 days, at 
D per cent. per annum, and change it to 4 and 6 per cent. 
per annum. at 5 per cent. $79.861. 
Ans, 4 at 4 per cent. $63.891. 
) at 6 per cent. $95.831. 
103. Find the interest of $725.50 for 150 days, at 7 
per cent. per annum, and change it to 6 and 8 per cent. 
per annum, at '7 per cent. $21.16. 
A ! at 6 per cent. $18.14. 
at 8 per cent. $24.18. 


Art. 207. To find the interest when 365 days is con- 
sidered as a year, 


*“Rute.—Find the interest for one year and multiply it 
by the number of years and fractional parts of a year. 


104. What is the interest of $250 for 60 days, at 7 


per cent. per annum ? Ans, $2.88. 
105. What is the interest of® $600 for 90 days, at 6 

per cent. per annum ? Ans. $8.88. 
106. What is the amount of $350 for 75 hae ai 8 

per cent. per annum ? Ans. 355.7 
eee What is the amount of $1000 for 100 fie at 
} per cent. per annum ? Ans. $1017.81. 


108. What is the amourt of £100 for 60 days, at 53 
per cent. per annum ? Ans. £109. 0s. 9$d.. 


PROBLEMS. 171 


109. What is the amount of $269.50 for 120 days, at 


7 per cent. per annum ? + Ans. $275.70. 
110. What is the amount of $3175.25 for 180 days, 
at 6 per cent. per annum ? Ans. $8269.21, 
111. What is the interest of $10000 for 40 days, at 5 
per cent. per annum ? Ans. $54.79. 
112, What is the interest of £1225. 10s. for 30 days, 
at 10 per cent. per annum ? Ans. £10. 1s. 23d. 


113. What is the interest of £2016. 18s. 9d. for 45 
days, at 8 per cent. per annum ? 
Ans. £19. 17s. 104d+. 

114. What is the amount of $3110.45 for 90 days, at 
53 per cent. per annum ? Ans. $3152.77, 

115. What is the amount of $1 for 75 days, at 6 per 
cent. per annum ? Ans. $1.01. 

116. What is the amount of £1 for 150 days, at 84 
per cent. per annum ? Ans. £1. 0s. 84d. 


PROBLEMS. 


Arr. 208. To find the rate per cent., when the princi- 
pal, interest, and time are given, 


Ruiz.—find the interest of the principal at one per 
cent. perannum, for the given time, and divide it into the 
given interest ; the quotient will be the rate per cent. 


117. The interest of $250 dollars for 2 years was $30; 
what was the rate per cent. per annum ? 
Ans. 6 pr, ct. 
118. The interest of $1750 for 80 days was $13.123 


what was the rate per cent. per annum ? 
Ans. 9 pr. ct. 


172 INTEREST, 


119. The interest of $78.75 for 1 yr. 9 mo. was 
$5.5125 ; what was the rate per cent. per annum ? 
- Ans, 4 pr. ct. 


120. $1000 was put out at interest for 2 yr. 8mo.; 
the interest during that time was $200; what was the 
rate per cent. per annum ? Ans. 73 pr. ct, 


121. The interest of $2100 for 3 yr. 1 mo. 20 days 

was $296.625 ; what was the rate per cent. per annum ? 
Ans. 43 pr. ct. 

122. In’ 9 months the interest on £1829. 10s. was 


£68. 12s. 14d. ;, what was the rate per cent. per annum ? 
Ans. 5 pr. ct. 


123. In lyr. 4 mo., $7500 amounted to $7850; what 
was the rate per cent. per annum? . Ans. 33 pr. ct. 


124. If £688. 2s. 6d. yield £82. 11s. 6d. interest in 


1 yr. 6 mo., what is the rate per cent. per annum ? 
Ans, 8 pr, ct: 


Art. 209. To find the time, when the principal, inter- 
est, and rate per cent. per annum are given, 

Rutz.—Find the interest of the given principal for one 
year at the given rate per cent. per annum, and divide it 
into the given interest ; the quotient will be the time in 
years, , 

125. The interest of $200 for a certain period of time, 


at 6 per cent. per annum, was $30; what was the time? 
Ans. 2 yr. 6 mos, 


126. At the rate of 7 per cent. per annum, the inter- 
est of $3060 was $642.60; what was the time ? 
Ans. 3 yrs. 


127. The interest of £432. 15s. for a certain time, 
at 6 per cent. per annum, was £129. 16s. 6d.; what was 
the time ? : Ans. 5 years. 


128. At the rate of 4} per cent. per annum the inte 


rest of $600 was $2.25; what was the time ? 
Ans. 30 days. 


PARTIAL PAYMENTS, 173 


129. The amount of $765.60, at 7 per cent. per 
anpum, was $772.299, what was the time? 
Ans. 45 days. 


130. The amount of £1021 17s. 6d. for a certain time 
at 5 per cent. per annum, was £1098 10s. 53d.; what 
was the time ? Ans. 1 yr. 6 mo. 


Art. 210. To find the principal, when the interest, 
rate per cent. and time are given, 


Rurz.—find the interest of $1, for the given time and 
rate per cent. and divide it into the given interest. 


131. The interest of a certain sum of money for 2 
years, at 6 per cent. per annum, was $60; what was the 
principal ? Ans. $500. 


132. The interest of a sum of money for 9 months, 
at 7 per cent. per annum, was $126; what was the prin- 
cipal ? Ans, $2400. 

133. The interest of a sum of money for 1 yr. 6 mo., 
at 8 per cent. per annum, was $195 ; what was the prin- 
cipal ? Ans. $1625. 

134. If the interest of a sum of money for 3 yr. 4 mo., 
at 6 per cent. per annum is $142.73, what is the princi- 
pal Ans. $713.65. 

135. The interest of a sum of money was £370 10s., 
the time 2 yr. 4 mo. 15 days, and the rate, 4 per cent. 
per annum ; what was the principal? Ans. £3900. 


Notr.—There isone more problem, viz.: when the amount, time and rate 
percent. are given, to find the principal ; this is the rule of discount, 2 and will 
be treated of under that name. 


PART.) A PAs Yank PeNen o: 
Arr, 211. What is the United States’ rule for casting 
interest, when partial payments are made ? 


Ruize.—Apply the payment in the first place to the inte. 
rest then due, 
15* 


174 INTEREST. 


If the payment exceeds the interest, the surplus goes lo- 
wurds discharging the principal, and the subsequent inte. 
rest is to be computed on the balance of principal remain- 
ing due, 

‘Tf the payment be less than the interest, the surplus 
must not be taken to augment the principal ; but interest 
continues on the former principal until the period when the 
payments, taken together, exceed the interest due, and then 
the surplus is to be applied towards discharging the princi- 


pal, and the interest is to be computed on the balance, as 
aforesaid, 


(136.) 
$700. New Yorks, July 1st, 1849. 


For value received, I promise to pay to James Brown, 
or order, seven hundred dollars, on démand, with inte 
rest, at 7 per cent. per annum. 


On this note were the following endorsements. 
July Ist, 1850, $200. 
July Ist, 1851, $400. 


How much was due July Ist, 1852? 
Ans. $200.55+. 


(137.) 


$500. New Yorks, Jan. 1st, 1850. 


On demand, I promise to pay to C. G. Murch, five 
hundred dollars, with interest, at 6 per cent., value 


received. JAS. THOMEeen 


On this note were the following endorsements. 
Jan. Ist, 1851, $300. 
Jan. Ist, 1852, $200. 


How much is due Jan, Ist, 1853 ? 
| Ans. $46.428 


PARTIAL PAYMENTS. 175 


(138.) 
$2000. New Yorks, May Ist, 1850 
On demand, I promise to pay to Edward Brown, tws 
thousand dollars, with interest at7 per cent., value re- 
ceived, Joun Prrerson. 
On this note were the following endorsements : 
May Ist, 1851, $500. 
May Ist, 1852, $450. 
May Ist, 1853, $750. 
May Ist, 1854, $400. 
What will be due May Ist, 1855? Ans. $311.761. 


(139.) 
$1000. New York, Aug. 1, 1850. 


On demand, I promise to pay Seneca Solomon, one 
thousand dollars, with interest at 5 per cent., value re- 
ceived. Junius DusEenpury. 


On this note were the followirg endorsements : 


Dec. Ist, 1850, $310.25. 
April Ist, 1851, $225.50. 
Aug. Ist, 1852, $400.00 


What was due January Ist, 1853? Ans, $128.151. 


(140.) 
500. New Yorks, Jan. Ist, 1853. 


On demand, I promise to pay James Sweet, five hun 
dred dollars, with interest at 6 per cent., value received, 
STEPHEN JONES, 


On this note were the following endorsements : 
March Ist, $50. 
March 15th, $150. 
June 15th, $200. 
Oct. Ist, $50. 
What was the balance ? Ans. $62.607+. 


176 INTEREST. 


: (141.) 
$495.50. ; New York, Sept. 3d, 1852. 


On demand, I promise to pay to James Anderson, four 
hundred and ninety-five ;3%, with interest at 8 per cent., 
value received. PrTerR SMart. 


On this note were the following endorsements : 
Jan. Ist, 1853, $200. 
May 18th, “ $200. 
What was the balance January Ist, ee 
ns. 


(142.) 
$3000. New Yorks, Sept. 23, 1829. 


On demand, I promise to pay to Jones, Osborn & Co. , 
three thousand dollars, with interest at 6 per cent., va- 
lue received. Tompson Wuirz. 


On this bill were the following endorsements : 


Sept. 23d, 1831, $1000. 
‘ Jan’y 28d, 1882, $705.50. 

Aug. 10th, 1832, $750. 

July 19th,1833, the balance was paid. 
What was it ? Ans. 


COMPOUND INTEREST. 
Arr. 212. What is Compound Interest ? 


Compound interest is when the amount at the end of 
each year becomes the principal for the succeeding year. 


_ Arr. 213. To find the compound interest of any sum 
of money, 


Ruize.—TLind the amount of the given sum for one year ; 
call this amount a new principal for the second year and 


COMPOUND INTEREST. 173 


Jind its umount for one year ; the result will be the com- 
pound amount of the given principal for two years ; call 
this second amount a principal for the third year, and so 
proceed as many times as there are years ; the last amount 
well be the compound amount, and from it subtract the 
gwen principal ; the remainder will be the compound in- 
terest, 


1. What is the compound interest of $300 for 3 years, 
at 6 per cent. per annum ? Ans. $57.38048. 


2. What is the compound interest of $10000, for 3 
years, at 7 per cent. per annum ? Ans. $2250.43. 

3. What is the compound interest of £320, for 5 
years, at 5 per cent. per annum? Ans. £88 8s. 24d.+ 

4, What is the compound amount of £450, for 3 
years, at 10 per cent. per annum ? Ans. £598 19s. 

5. What is the compound amount of $200, for 2 years, 
at 74 per cent. per annum ? Ans. $231,124. 


6. What is the compound amount of £250, for 4 years, 
at 8 per cent. per annum ¢ Ans, £340 2s. 5}d.+ 


Art. 214, To find the compound interest, when there 
are vears and parts of a year, 


Ruite.—Find the amount as many times as there are 
whole years ; then find the amount of this amount for the 
partial year. 


7. What is the compound interest of $500 for 21 


years, at 5 per cent. per annum ? Ans. $65.034. 
8. What is the compound interest of $400 for 2 yrs 
J mos., at 6 per cent. per annum ? Ans. $69.67, 


9. What i is the compound amount of $250 for 3 yr. 2 
mo. 20 da., at 8 per cent. per annum? Ans. $320.526. 


10, Find the compound amount of £300 for 2 yr. 7 


mo. 15 da., at 5 per cent. per annum. 
Ans, £341 1s, 84d. 


178 DISCOUNT. 


11. What is the compound interest of £224 17s. 6d. 
for 5 yr. 6 mo., at 7 per cent. per annum ? 
Ans. £60 4s, 114d. 


ee 


DLS CoO UNe a 


Art, 215, What is Discount ? | 

Discount is an allowance made for the payment of money 
before it rs due. 

Arr. 216, How many kinds of discount are there ? 

Two: Bank and True Discount. 


Art. 217, To find the bank discount on any sum of 
money, 


Rutz.—Find the interest of the given sum for 3 days 
more than the given time, at the yiven rate per cent. per 


annum ; the result will be the bank discount. 

Norre.—The three days are called days of grace. It is customary for banks 
and merchants to allow notes torun 3 days iongerthan the specified time, and 
they always charge interest for those days. ‘The discount or present worth 


| or £1 is carried out very particularly, because it is often used as a unit of 
comparison, especially when a divisor. 


Art. 218. What is meant by the term present worth ? 


Lt is that which remains after the discount is subtractea 
from the given sum. 


Arr. 219, What is the result sometimes called ? 
Tt ts called the cash value. 


1. What is the bank discount on a note for $1, for 60 


days, at 6 per cent per annum ? Ans. $.0105. 
2. What is the bank discount on a note for $1, for 30 
days, at 74 per cent. per annum ? Ans. $.0062. 


3. What is the bank discount on a note for $1, for 45 
days, at 74 per cent. per annum ? Ans, 8.01. 


DISCOUNT. 1/9 


4, What is the bank discount on a note for £1, for 90 
days, at 8 per cent per annum ? 4 
‘Ans. £.02;¢ or, 4d. 3.8 far. 
5. What is the bank discount on a note for $100, for 
4 mo., at 6 per cent per annum 2? Ans. $2.05. 


6. What is the bank discount ona note for £100, pay 


able in 6 mo., at 10 per cent. per annum? 
Ans. £5 1s. 8d. 


7. What is the bank discount on a note for £200 pay 


able in 5 mo., at 9 per cent. per annum ? 
Ans. £7 13s. 


8. What is the bank discount and present worth of a 
note for $300, payable in 9 mo., at 53 per cent. per 
annum ? 

aie $12.512 discount. 
’ | $287.487 present worth. 


9. What is the bank discount and present worth of a 
note for $500, payable in 81 mo., at 64 per cent. per 


annum 2 
‘Ate $23.29 discount. 
* | $476.71 present worth. 


10. What is the bank discount and present worth of 
a £1000 note, payable in 75 days, at 85 per cent. per- 
annum ? 
ie £18 8s. 3d.+ discount. 
‘( £981 11s. 8d.+ present worth. 


11. What is the present worth of a $10 000 note, pay 
able in 2 mo., at 74 per cent. per annum ? 
Ans. $9868.75. 
12, What is the present worth and bank discount of s 
note for $250, payable in 1 mo., at 5 per cent. per annum 2 
Ans, § 2248-854 present worth. 
 ( $1.145 discount. 
13. What is the bank discount of a note for £3850, 


payable in 50 days, at 10 per cent. per annum ? 
Ans. £5. 3s. 02d. discount. 


180 DISCOUNT. 


14. What is the present worth and discount of a 
note for £450 in ] year, at 54 per cent. per annum } * 
Ans, 1 #425. 08: 104d. present worth. 
"(| £24 19s. 13d. discount. 


15. What is the bank discount and present worth of 
a note for $750.50, payable in 8 mo., at 6 per cent. per 
annum? =; Ay $11.632 discount. 
“~~ | $738.867 present worth. 


16. What is the bank discount and present worth 
of a note for $3150.25, payable in 60 days, at 62 per 
cent. per annum? 4, § $37.212 discount. 

’ | $3113.038 present worth. 


17. What is the present worth of a note for £80 12s., 
payable in 30 days, at 9 per cent. per annum ? 
ae £0 13s. 34d.+ discount. 
"(| £79 18s. 8td.+ present worth. - 


18.. What is the bank discount and cash value of a 
note for $1728, payable in 20 days, at 54 per cent. per 
annum ? rer $6.072 bank discount. 

1 $1721.928 cash value. 


19. Find the bank discount and cash value of a note 
for £112 10s., payable in 30 days, at 94 per cent. per 
annum ? ee £0 19s. 74d. bank discount. 

*( £111 10s. 43d. cash value. 


20. How much cash is equivalent to a note for 
$725.80, due in six months, at 5} per cent. per annum? 
Ans. $705.508. 


21. How much cash is equivalent to a note for 

$1255.88, payable in 4 mo., at 7 per cent. per annum? 
Ans. $1225.355. 

22. What is the present value of a note for £680. 

12s. 6d., payable 10 mo. hence, at 8 per cent. per an- 
num ? Ans. £634 15s, 1ld.+ 


23. On the Ist of January, 1853, a note for $1000 
was given, to be paid on the 1st of May ensuing; what 
was its cash value, at 7 per cent. Aus. $976.083. 


DISCOUNT. 18] 


24. A note of $2310 was to be paid on the Ist of Octv- 
ber, 1852; what was its value on the Ist of June, 1852, 
at 6 per cent. per annum ? Ans. $2262.64. 


25. A note for $500, due 138th of August, 1853, was 
paid. on the first day of July, 1853; how much was 
thrown off the face of the note for payment before due, 
reckoning interest at 7 per cent. per annum ? 

Ans. $4.47%. 

26. A note for £351. 11s. was taken up 2 mo. 20 days 
before due; what was paid, and what thrown off the face 
of the note, interest at 5 per cent. per annum ? 

a £347. 9s. 113d. cash value, 
ja £4, 1s. Odd. discount 
. Ls, 04d. 


27. A flour merchant bought 75 bafrels of flour at 
$4.50 per barrel, on a credit of 3 mo., 6 per cent. per 
annum. Instead of waiting 3 mo., he paid the bill in 
cash; how much was thrown off, and how much paid ? 

ree $332.27 cash, 
* 1 $5.23 discount. 


28. A merchant bought for cash, 300 barrels of pork, 
at $10.50 per barrel; he sold them the same day at $12 
per barrel, on a note for 3 mo., at 7 per cent. per an- 
num ; what was the cash value of the sale, and how much 
did he make ? ye $3534.90 cash value, 

"1 $384.90 gain. 


29. A speculator bought 100 bales of cotton, each bale 
596 lb., at 8 cents per lb., on a note for 8 mo., 7} per 
cent. per annum ; he immediately sold the entire lot for 
$5000 cash, and paid his note; how much did he gain ? 

Ans. $473.38. 

30. A butter dealer bought for cash, 78 firkins of but- 
ter, 56 lb. each, at 25 cents a pound. He sold them the 
same day at 254 cents per lb., on a note for 4 mo., at 8 
per cent. per annum; did he gain or lose by the opera- 
tion, and how much? ‘Ans, $8.60 lost. 


31. I bought 2000 tons of coal at $3.50 per ton, 
16 


182 DISCOUNT. 


on my note for 6 months, and sold them for the same 
price, on a note for 38 mo.; what was my cash gain. at 73 
per cent. per annum ? Ans, $131.25. 


32. A man bought a house valued at $5000, on the 
following terms ;: $2500 in cash, $1250 in 8 months, and 
the balance in 6 months, interest being 5 per cent. per 


annum ; what was the cash value of the house ? 
Ans. $4952.08. 


33, A person owed $1400, payable in 7 mo., at 44 
per cent. per annum; he paid it in4 mo. after date. 
How much was taken off the face of the note for pay- 
ment before due ? Ans. $15.75. 


34, What is the worth of the following notes at 7 per 
cent. per annum ? 7 


(34.) | 

$100. Sixty days after date, I promise to pay to the 

order of Solomon Levi, one hundred dollars, value re- 
ceived. Isaac SEAMAN. 
Ans. $98.77. 


35. 
$296.50. Six months ae date, I promise te pay to 
the order of C. C. Churchill, two hundred and ninety- 
six7?°, dollars, value received. 
AsrauamM Van Horn. 


Ans. $285.95. 


36. 
$3152.67. Three BS. Hes date, I promise to pay 
to the order of Job Hicks, three thousand one hundred 
and fifty-two 8 dollars, value received. 
JEREMIAH Hossoy. 


Ans. $3095.66. 


Art. 220. What is the true present worth of any sum 
of money ? 


Lt is a sum which, if put at interest, will amount to the 
given sum at the given rate per cent. and time. 


DISCOUNT.. 183 


Art. 221. To find the true present worth, 


Ruie.— Divide the given sum by the amount of $1 or, 
£1, at the given rate per cent. and for the time; the quo: 
tient will be the true present worth. 


Arr. 222. What is the true discount 2 


It ts the difference between the true present worth and the 
given sum. 


37. What is the true present worth of $104, payable 
in 8 mo., at 6 per cent. per annum ? Ans. $100. 
38. What is the true present worth and discount of 
$315, payable in 10 mo., at 6 per cent. per annum ? 
Tete $300 present worth. 
"1 $15 discount. 
39. What is the true present worth and discount of 
£621, payable in 6 mo., at 7 per cent. per annum ? 
Ans, ) £900 present worth. 
* | £21 discount. 


40. What is the true discount of $526.25, payable in 
9 mo., at 7 per cent. per annum ? Ans. $26.25. 


41. What is the true present worth of $4363.20, pay 
able in 3 mo., at 4 per cent. per annum? 
Ans. $4320. 


42. What is the present worth of $1318.80, payable 
in 7 mo., at 8 per cent. per annum ? Ans. $1260. 


43. What is the present worth and discount of £3172, 
payable in 8 mo., at 62 per cent. per annum ? 
am £3120 present worth. 
Ds. ; 
£52 discount. 


44, What is the present worth of $5160, payable in 4 
mo., 24 days, at 8 per cent. per annum? Ans. $5000. 


45, What is the discount of $721, pavable in 7 mo. 6 
days, at 5 per cent. per arnum ? Ans. $21. 


184 - - pISCOUNT. 


46. Whatis the present worth and discount of $225.96, 
payable in 8 mo., at 74 per cent. per annum ? 
$215.20 present worth, 
Ans : 
* | $10.76 discount. 
47, What is the cash value of $4987.50, payable in 7 
mo. 15 days, at 61 per cent. per annum ? 
Ans. $4800. 
48. What is the cash value of $4000, payable in 1 
yr. 7 mo., at 4 per. cent. per annum ? 
Ans. $3761.757. 
49. What is the cash value of £2400, payable in 8 yr. 
6 mo., at 8 per cent. per annum ? Ans. £1875. 


50. What is the cash value and discount of £300, pay- 
able in 1 yr. 5 mo., at 6 per cent. per annum? 
Pe 1 £276 9s. 114d.+ pregent worth. 
™ 1 £23 10s. 04d.+ discount. 


51. What sum of money will amount to $5000 in 2 
yr. 7 mo. 12 days, at 12 per cent. per annum ? 
Ans. $3805.17 


52. What is the present worth and discount on $1500, 
payable in 1 yr. 2 mo. 20 days, at 7 per cent. per 
annum ? 

eae § $1381.78 present worth. 
* 1 $118.22 discount. 


_. 58. Wuat sum of money will in 2 yr. 1 mo., at 6 per 
cent. per annum, ‘amount to $2261.25? Ans, 2010. 
54. What sum of money will amount to £120 13s. 4d. 
in 10 mo., at $8 per cent. per annum ? 
Ans. £113 2s. 6d. 


55. What sum will amount to $1875.20 in 4 mo. 18 
days, at 61 per cent. per annum? Ans. $1343.023. 


56. What sum of mony will, in 60 days, amount to 
$14229.60, at 5 per cent. per annum ? | 
Ans, $14112, 


DISCOUNT. 185 
57. What sum of money will amount to £500 in 2 yr. 
11 mo. at 74 per cent. per annum? Ans. £410 ds. lid. 


58. What is the present worth of $3000, one half pay- 
able in 6 mos. and the other half payable in 9 mos., at 5 
per cent. per annum ? Ans. $2909. 197, 


09. What is the present worth of $4000, one quarter 
payable in 1 yr. and the remainder in 1 yr. 6 mo., at 6 
per cent. per annum ? Ans, $2695. 68. 


60. What is the present worth of £7500, £4000 pay- 
able in 7 mo., at 74 per cent. per annum, and the remain- 
der payable in 10 mo. ., at 44 per cent. per annum ? 

Ans. £7205 168. 7d.+ 


61. The sum of $10 000 is to be paid by four equal 
instalments; the first in 3 mo., the second in 6 mo., the 
third in 9 mo., and the fourth, in 1 year; what is the 
present worth of the $10000, at 6 per cent. per annum ? 

Ans. $9641.073+. 


62. When money is 2 per cent. a month, what sum is 
equivalent to $1850, payable in 15 days ? 
Ans, $1836.63. 


63. What money is worth $1600, payable in 5 mo., 


‘at 14 per cent. a month ? Ans. $1488.37. 
64. A person made an investment of money, on which 

he lost 10 per cent. He received $4500 of his money 

back; how much did he invest ? Ans. $5000. 


65. On the 16th of August, 1829, [ promise to pay 
$1050.69; what sum will be equivalent to the above 
sum, on July Ist, 1826, at 6 per cent. per annum ? 

| Ans, $884.79. 

66. A merchant had a note of $1400, to pay on the 
Ist of Aug. 1858; he paid it on the 15th of May, 1853 ; 
what sum did he pay, interest 7 per cent. per annum ? 

Ans, $1379.61. 

67. On making up my accounts on the Ist of July, 
1850, I find that Lowe two bills ; ; one pay able on the 18th 
of December, 1850, and the other on the 27th of January, 

16* 


156 | )), DISCOUNT. 
i! ‘ 

1851. The fist is for $1769.20, and the second for 
$2000; what is the value of the two notes, July 1st, 
1850, at 6 per cent. per annum? Ans. $8656.305. 

68. A person put a sum of money out at interest for 
3 mo. at.7 per cent. per annum, and received for princi- 
pal and interest £760 15s. 8d. ; what was the sum ? 

Ans. £747 13s. 84d. 


69. If I receive $20160, which is my own money, 
und 20 per cent. over; what is my own money ? 
Ans. $16800. 
70. What is the present worth of $12000, 3 of which 
is payable in 6 mo., 4 in 10 mo., and the remainder in 
15 mo., interest being 9 per cent. per annum ? 
Ans. $11260.51. 


71. I owe $500, payable in 2 mo., $350, payable in 
6 mo.; what is the present worth of the whole amount, 
interest, 41 per cent. per annum? Ans. $8388.575. 


72. A merchant owes $1000, payable on the 15th 
August, 1853; $500, payable on the 10th of Oct., 1853 ; 
$900, payable on the Ist of Nov. 1853; what is the 
value of the three notes, on the Ist of July, 1853, at 6 
per cent. per annum ? Ans. $2366.79. 

73. There are two notes, one for $162.75, payable 
Ist. Jan., 1851, and the other for $910, payable May 
Ist, 1851; what is the value of the two notes on the Ist 
of March, 1851, interest 74 per cent. per annum ? 

Ans. $1065.58. 


74. What is the difference between the true and bank 
discount on $7000, payable in 7 mo., at 6 per cent. per 
annum ? Ans. $11.785. 

75. What is the difference between the true and bank 
discount on $10000 payable in 45 mo., at 8 per cent. 
per annum ? : Ans. $15.404. 

76. What is the difference between the true and. bank 
discount on £2118 7s. 10d. payable in 1 yr. 20 days, at 
7 per cent. per annum ? Ans, £10 15s. 11.754. 


ms 
PROFIT AND LOSS. 187 


77. Which is the more advantageous, to buy muslin 
at 72 cts. per yd. on 4 mo., or 8 cts. per yd. on 6 mo.,, 
at 6 per cent. per annum ? Ans. 74 cts. a yard. 

78. After 10 per cent. had been cut from a piece of 


cloth, there remained 47,5 yd.; how long was the piece 
of cloth before any was cut off ? ans. 53 yards. 


PROFIT AND LOSS. 
Arr. 223. What is Profit and Loss ? 


Profit and loss is a rule by which it is found what is 
gained or lost in various transactions. 


Arr. 224. To find the profit and loss when the cost 
and selling prices are given, 


Ru.e.—Subtract the less sum from the greater ; tf the 
cost be the less, the remainder will be the gain ; if the cost 
be the greater, the remainder will be the loss. 


1. A man bought a house for $3725, and sold it for 


$4000; how much did he make ? Ans. $275. 
2. Bought a horse for $275.80, and sold him for $262. 
50; what was lost ? Ans. $13.80, 


3. A person bought 350 barrels of flour, for which he 
paid $6 per barrel, and sold them at $7 a barrel; what 
did he gain ? Ans. $350. 

4, A man bought a house worth $1100, for 20000 feet 
of lumber that cost him $42.90 a thousand ; what did he 
make by the exchange ? Ans. $242. 

5. A sold to B, 150 A. 2 roods of land for $65000; 
the land cost $300 per acre; how much did A gain? 

Ans. $19850, 

6. A man bought 54 T. 13 ewt. 56 Ib. of iron for 2} 
cents per pound, and sold it at $50 a ton ; how much did 
he gain ? Ans. $273.39. 


st 


188 PROFIT. AND LOSS. ‘ 


7. { exchanged 58 ewt. 2 qr. 21 lb. of iron, which cost 
$3.20 a cwt., 350 bushels of potatoes, worth 984 cents a 
bushel ; did I gain or lose, and how much ? 

Ans, $156.878 gam. 

8, A man bought a farm for $1650; he kept it cne 
year, and sold it for $2000; how much did he make, al- 
lowing interest at 7 per cent. per annum, while hée kept 
the farm ? Ans. $234.50 gain. 


9. A person bought 26 hhd. of sugar, averaging 1300 
lb. a hhd., for '7 cents a pound; he refined it at an ex- 
pense of $8388; during the process of refining 26 Jb. 
were wasted on each hhd. ; he then sold it at 101 cents 
a pound; how much did he gain? , 

Ans, $774.02. 


10. Bought 14 hhd. of wine for $1200, and retailed 
it $2.25 a gallon; allowing 38 gallons for leakage on each 
hogshead, how much did I gain ? Ans. $690 gain. 

11. A provision merchant packed 100 hogs, averaging 
150 Ib. each, at a cost of 9 cents a pound for the pork 
and 50 cents a head for cutting and packing; how much 
will he make if he sells the lot at 124 cents a pound ? 

Ans. $475 gain. 


Art. 225. To find the selling price, when the cost and 
gain or loss are given, ; 


Ruitx.—Add the gain to, or subtract the loss from the 
cost, and the result will be the selling price. 


Art. 226. To find the cost, when the selling price and 
he gain or loss are given, 


Rvuis.—Subtract the gain from, or add the loss to the 
selling price, and the result will be the cost. 


12. A person bought a house for $5400, and sold it so 
as to make $429,874 ; for how much did he sell it 2 
Ans. $5829 374. 
13. A person bought a farm for £1612. 13s 104d, 


PROFIT AND LOSS. 189 


and sold it at a sacrifice of £211. 18s. 9d.; for how much 
was it sold ? Ans. £1400. 15s. 14d. 


14, A merchant sold 25 pieces of cloth at $43.75 a 
piece, and by so doing he lost $229.50; for how much 
did he buy it? Ans. $1323.25. 

15, A person sold 156 A. 3 R. 12 sq. p. of land at 
$750 per acre, and cleared $14000; how much was the 
cost ? Ans, $108618.75. 


16. A merchant bought 325 barrels of pork at $17.50 
per barrel, and sold them so as to make 14 cents a pound 3 
for how much did he sell the whole ? 

Ans. $6500. 


17. A grocer bought 15 hhd. of sugar, each weighing 
13 cwt. 1 qr. 17 1b., at $7.50 per ewt., and sold them so 
as to make 24 cents on a pound; for how much was ove 
pound sold, and for how much was the whole sold ? 

Ans, } 19 cents per pound, 
$2013 whole. 

18. A merchant sold 73 pieces of linen, each 18 yd. 
3 qr. 1 na., for $1000, ea thereby gained 25 cenis a 
yard ; what did the whole cost ? 

Ans. $747.921. 


Arr. 227. To find the gain or loss, when the cost and 
the gain or loss per cent. are given, 


Rutz.—Multiply the cost by the gain or loss per cent., 
and the product will be the gain or loss. 


19. A person entered into a speculation, in which he 
invested $7500; he cleared 20 perveent., how much did 
he make? Ans. $1500. 


20, Bought a horse for $306, and sold him at 10 per 
cent. advance ; how much was gained, and what was the 
horse sold for ? Ans. $30.60 gained. 

The horse was sold for $336.60. 


21. Bought a yard of cloth for $6, and sold it at 163 


190 PROFIT AND LOSS. 


per cent. profit; what was made on the yard of cloth, and 
tor how much was it sold ? ON j $1 gained, 
ps. : 
| $7 a yard. 


22. A person entered into business with a capital of 
$2335.50; in one year he augmented it 334 per cent. ; 
what was his capital at the commencement of the follow- 
ing year? Ans, $3114. 


23, Bought a hogshead of sugar weighing 1280 Ib., at 
74 cents per pound,.and sold it at 25 per cent. profit ; 
for how much was it sold ? 


Ans, $120. 


24, What is 372 per cent. advance on $1385.50 ? 
Ans, $1905.064. 


25. A person invested £698. 10s. 6d. in a shipment to 
Canton, on which he made 112% per cent. ; how .much 
did he.gain ? Ans. £785. 16s. 93d. 


26. Bought a quantity of drugs, amounting to £150. 
11s., and sold them at 250 per cent. profit; what was 
the profit ? Ans. £376. 7s. 6d. 


27. A merchant had a stock of goods amounting to 
$3750 ; a fire destroyed 662 per cent. of his stock ; not 
being insured, how much did he lose? —Ans, $2500. 


28. In the previous sum, suppose the merchant was 
fully insured at selling prices, say 20 per cent. advance 
on $3750, insurance being 11 per cent., how much would 
he make by being burned out, instead of waiting 6 
months to sell the same goods at the same advance, when 
money is worth 7 percent. per annum ? 


Ans. $8'7.637. 


29. A cotton factory valued at $8000, and its contents 
worth $13500 caught fire; the building was entirely 
destroyed, and 60 per cent. of the contents were saved ; 
what was the total loss ? Ans. $13400. 


30. I lent a friend $50 and lost 100 per cent. of it; 
how much did I receive ? Ans. Nothing. 


PROFIT AND LOSS, 19; 


31. A person entered into business with a capital of 
$2310; in 2 years he increased it 482 per cent.; what 
was his capital then ? Ans. $3426.50. 


32. Bought 500 bags of coffee, each bag 49+ Ib., at 
12 cts. a pound, and sold the whole at 162 per cent. 
profit ; how much was it sold for? Ans. $3447.50. 


53. A merchant bought 3875 T. 15 ewt. of wool, at 
$75 per ton, and sold it so as to make 20 per cent. ; for 
how much per ewt. did he sell it ? Ans, 4.50. 


34. A grocer bought 410 bu. 3 pk. 4 qt. of potatoes, 
96 cts. per bushel ; at how much per quart must he sell 
them so as to make 124 per cent ? Ans $.082. 


Art. 228. To find the gain or loss per cent., when the 
cost and the gain or loss are known, 


Ruie.— Consider the gain or loss on a single or a num- 
ber of articles as the numerator of a fraction, and the cost of 
the same article or articles as the denominator ; reduce both 
terms of the fraction tothe same denomination, and then to 
hundredths ; and the quotient will be the gain or loss per 
cent: 


35. Bought sugar at 10 cts. per pound, and sold at 
12 cts. per pound; how much per cent. was gained ? 
Ans. 20 per cent. 


36. A cow was bought for $40, and sold for $35; 
how much per cent. was lost ? Ans, 123 per cent. 


37. I bought a horse for $320, and sold him for $450 ; 
how much per cent. did make? Ans, 402 per cent. 


38. A person bought 20 reams of paper, at $2 per 
ream, and sold it for 18 cts. per quire; how much per 
cent was gained ? Ans. 80 per cent. 


39. A flour merchant bought 300 barrels of flour for 
$1590, and sold it for $6 per barrel’ how much per cent, 


4 
192 PROFIT AND LOSS. 


did he make on the lot, and how much per cent. did he 
make on a single barrel ? Ans. 1334 per cent. 

40. A person bought a barrel of pork for $11.25, and 
sold it for $13 ; how much per cent did he make ? 


Ans. 155 per cent. 


41. Bought 3 hhd. of sugar, each-18 ewt. 3 qr. 14 Ib., 
at $8 per ewt., and sold it for 10 cts. per pound; how 
much per cent. was made ? 

Ans. 25 per cent. 


42..A grocer bought 1 barrel of flour for $6, and sold 
it at 28 cts. for '7 lb. ; how much per cent. did he make ? 
Ans. 502 per cent. 


43. A man bought a house for $5000, and sold it for 
$4225; how much per cent. did he lose ? 
Ans. 154 per cent. 


44, An iron dealer bought 45 T. 16 ewt. 25 1b. of iron, 
at $75 per ton, and sold it for $78.50 per ton; how 
much, and how much per cent. did he make ? 

Ans, 1 3160.848 total gain. 
' (42 per cent. 


Arr. 229. To find the cost when the selling price and 
the gain or loss per cent. are given, 


Ruie.—Divide the selling price by 1, increased by the 
guin rer cent., or diminish by the loss per cent. ; the quo- 
tient will be the cost or buying price, 


45, A man sold a horse for 315, and made 5 per cent. 
for how much did he buy him 2 Ans. $300. 


46, A merchant received $450 for the proceeds of a 
speculation, in which he lost 10 per cent. ; how much did” 
he invest ? Ans. $500. 

47, Sold 20 barrels of flour for $74 per barrel and 
made 25 per cent ; how much did the 20 barrels of flour 
cost ? Ans. $120, 


PROFIT AND LOSS. 193 


48. Sold a house for $1250, and lost 4 per cent. by 
the transaction ; how much did the house cost? 
Ans. $1302.083. 


49, A grocer sold sugar at 8 cts. a pound, and made 


25 per cent. ; how much did it cost a pound ? , 
Ans. $.064, 


50. Sold 265 firkins of butter, at 25 cts. a pound, and 


made 12 per cent. ; what did the whole cost ? 
Ans. $312.50. 


D1. Sold, 78 ewt. 3 qr. 14 Ib. of sugar, at 8 cts. a 
pound, and gained 15 per cent.; how much did the 
whole cost ? Ans. $548.80. 


52. Sold 160 tierces of rice, each weighing 500 Ib., at 
71 cts, a pound, and gained 20 per cent.; what did the 
whole cost ? Ans. $4833.334. 


53. Sold 3 lots of ground: the first for $275, and 
made 30 per cent.; the second for $300, and made 50 
per cent.; and the third for 3500, and made 25 per cent. ; 
what did the three lots cost ? _ Ans, $811.538. 

54. Sold a farm, containing 62_.A. 3. R. 21 sq. p., for 
$275 an acre, and cleared 64 per cent.; what did the 
whole cost ? Ans. $16275.147. 


55. A merchant sold 700 barrels of flour for $4025, 
and gained 15 per cent.; how much a barrel did the 
flour cost ? Ans $5. 


56. A person laid in 25 tons of coal during the sum- 
mer; in winter the price of coal was $7.10 a ton; by 
laying it in in summer, he found he had saved 873 
per cent. ; how much did the coal cost? 
Ans. $129.09. 

57. A flour merchant bought 250 barrels of flour at 
$5.50 per barrel, and sold the whole for $1875; how 
much per cent. did he make ? 

Ans. 36,4 per cent. 


58. Bought a pipe of brandy for $2 per gallon, on a 
17 


194 PROFIT AND LOSS. 


note at 6 months, at 7 per cent., and sold it for $2.50 
cash per gallon ; how much per cent. was gained ? 
Ans. .2735; per cent.+. 


59. Bought 360 pieces of ribbon at $3.25 a piece, on 
a note for 7 months, at 6 per cent. per annum, and sold 
thém for $3.50 cash, per piece; how much and how 
much per cent. was made? 
a $131.58 gain, 
*( 112 per cent. (nearly.) 


Art. 230. When the selling price and the gain or loss 
per cent, are given, to find the gain or loss per cent. at 
some other selling price. 


Rurs.—Find the cost by means of the given selling price 
and rate per cent., and then compare the cost and the other 
selling price, and jind the gain or loss per cent. by Art. 
(228) 


60. A person sold a house for $3000 and gained 50 
per cent.; how much per cent. would he have made had 
he sold it for $2500? Ans. 25 per cent. 


61. A farmer sold 20 acres of land for $3800 an acre, 
and gained 25 per cent.; how much per cent. would he 
have gained or lost had he sold the land for $4000 2 

Ans. 162 per cent. loss. 


62. Sold 7800 bushels of rye for 50 cents a bushel, 
and lost 9 per cent.; how much per cent. would have 
been gained or lost, had the rye been sold for 60 cents a 
bushel ? Ans. 94 per cent. gain, 


63. A lumber merchant sold 49500 feet of lumber for 
#18 per thousand feet, and gained 20 per cent. ; how 
much per/cent. would he have made or lost, had he sold. 
at $16 per thousand feet? Ans, 62 per cent. profit. 


Art. 23]. When the selling price and its correspond- 
ing gain or loss per cent. are given, to find the selling 
price at some other gain or loss per cent., 


PROMISCUOUS EXAMPLES. 195 


Ruiz.—Find the cost frum the given selling price and 
sts corresponding gain or loss per cent.,and to the cost add 
the other percentage, if tt be gain,. or subtract, if loss ; 
the result will be the selling price required. 


64, A person sold a barrel of pork for $12, and gain- 
ed 20 per cent. ; for hw much would it have sold, had 
he gained 25 per cent, ' Ans. $12.50. 


65. A grocer ead coTee at 10 cents per pound, and 
gained GP per cent.; for how much must he sell it to 
gain 124 per cent. r Ans. 9 cents per pound. 


66. A machinist sold an engine for $24000, and lost 4 
per cent. ; for how much ought he to have sold it to gain 
10 per cent. ? Ans. $27500. 


67. A lumber dealer sold 12000 feet of boards at 

31.25 a thousand, and gained 25 per cent.; for how 
much a thousand would the boards have been ‘sold, had 
he gained 15 per cent. ? Ans. $28.75. 


os 


PROMISCUOUS EXAMPLES. 


68. A person bought 2 pieces of French broadcloth ; 
the first piece measured 87} aunes, and the second 392 
aunes; the cloth cost $4.62} a yard, and was sold for 
$5 a yard; how much did he make, counting an aune 
equal to 14 yard? Ans. $36.04. 

69. A farmer bought 752 bushels of rye at 874 cents 
a bushel, and sold itso as to make 16% per cent.; for 
how much did he sell the whole? * Ans. $32,975. 

70. A man bought a horse for $317.77, and sold him 
. for $800; how much per cent. did he lose ? 

Ans, 575; per cent. 

71. Bought 700 doz. of eggs at 12 cts., and sold them 
for 121 cts. a doz; how much was gained, and how 


h per cent. ? 33 
much per cent. ? see ae: gain. 
~ per cent. 


196 PROFIT AND LOSS, 


72. Sold 250 bushels of wheat at 20 shillings a bushel, 
and gained 10 per cent. ; what did the whole cost ? 


’ Ans, £227 5s. 53°;d. 

73. Sold a hogshead of wine at $21 a gallon, and lost. 
10 per cent., when it could have been sold at 50 per cent. 
advance; for how much under its value was the wine 


sold 2 Ans, $1.50. 


74. Sold a horse for $234, and gained 17 per cent., 
when he ought to have been sold at 25 per cent. profit; 
how much above the cost would the latter percentage 
give % Ans, $50. 


75. Bought 8000 bags of sugar, each bag 100 Ib., at 
61 cts., per pound on a note for 5 months, at 6 per cent. 
per annum, and sold the lot at the same price for cash; 
how much was gained ? Ans. $478.125. 


76. A person advanced $5000 in uncurrent money, to 
a contractor who was building a house; on this money 
there was a discount of 4 per cent.; the next day he 
received a check for $5000 in payment for what he had 
Jent; how much did he gain? Ans. $25. 


77. A flour merchant bought 400 barrels of flour, for 
$7 cash, a barrel; he sold it for 74 a barrel, on a note 
payable in 4 months, at 7 per cent. per annum; how 
much did he make ? Ans. $128.25. 


78. A tailor bought 500 yd. of cloth at $4.374 a yard, 
on a credit of 8 months, at 6 per cent. per annum, and 
sold the cloth at $4.50 a yard, on a credit of 3 months 
at the same rate per cent.; how much did he gain, in 
eash value ? Ans. $116.217. 


79. A liquor dealer bought a pipe of brandy at $2 a 
gallon, on a note at 6 months, 7 per cent. per annum 
and sold it at the same price a gallon, for cash; how 
much did he gain ? 

Ans. $8.967. 


80. Bought 360 pieces of ribbon at $3.25 a piece for 
cash; sold the ribbon at $3.50 a piece, on a note pay 


EXCHANGE. 197 


able in 7 months, at 5 per cent. per annum; how niuch 
was made; and how much per cent. ? 
$52.75 gain. 
ae i 44-+ per cent. 
81. A person bought 3 hhd. of sugar, each hogshead 
weighed 14121 Ib.; he sold it at 11 cts. a pound, and 
gained 374 per cent.; for how much ought it to have 
been sold, so as to gain 50 per cent., ard what did the 
whole cost ? Ans. 12 cts. a pound. 


82. A man bought a house, and sold it for $3225, by 
which he lost 4 per cent.; had he sold it at an advance 
of 74 per cent., how much would he have gained ? 

Ans. $251.953. 


83. A cotton broker bought 550 bales of cotton, each 
bale 128+ Ib.; he sold it at 10 cts. a pound, which was 
1 per cent. advance on the cost; had he waited a few 
days longer he might have made an extra ¢ per cent. ; 
for how much would the cotton then have been sold 2 

Ans. $39828.367. 


84. A merchant sold 1500 barrels of pork at $lllba 
barrel on a note for 3 months, at 54 per cent. per 
annum ; the profit was 20 per cent.; what did the pork 
cost ? Ans. $13862.70. 


85. A grocer sold 400 barrels of apples, for $3 a 
barrel, and lost 4 per cent. by the sale; what did the 
whole cost? Ans. $1250. 


EXCHANGE, 


Arr. 232. What is Exchange ? 

Hxchange is the method of finding the value of the cur 
rency of one country in that of another. 

Art. 233. What is the currency of a country ? 


It is the coins and bills that constitute the money of that 


country. 
Weg 


198 EXCHANGE. 
Art, 234. What is the rule for Exchange ? 


The value of a unit of the money of the various coun- 
tries being known, analysis will supply the rules for most 
cases. 


Art. 235. To reduce sterling money to Federal, 


Rutze.— Consider one dollar equivalent to nine sixpences 
Sterling ; then reduce the given amount to sixpences, di- 
vide by 9, and to this result add a certain given rate per 
cent. 


Note—The value of a pound sterling is fixed by Congress at $4.84. But 
among merchants and brokers, when Bills of Exchange are bought or sold, 


the old par value, $4.449 tothe pound sterling, is taken as the basis of cal- 
culation. and to this a certain percentage is added, which is not fixed, but va- 
ries with the fluctuations of trade. Nine per cent. is generally the rate, but 
it is sometimes a little more or less than 9 


1. Reduce £18 sterling to Federal money, without 


premium. Ans. $80. 

2. Reduce £45 sterling to Federal money, without 
premium. Ans. $200. 

3. Reduce £100 sterling to Federal money, without 
premium. Ans. $444.444, 

4, Reduce £384 sterling to Federal money, without 
premium. Ans. $1706.666 +. 

5. Reduce £18. 15s. sterling to Federal money, with 
out premium. Ans. $83.33. 

6. Reduce £711. 14s, 6d. sterling to Federal money, 

without premium. Ans, $3163.22, 

7%. Reduce £144. 19s. 104d. sterling to Federal mo- 
ney, without premium. Ans. $644.416+. 

8. Reduce £1. 10s. 93d. sterling to Federal money, 
without premium. Ans. $6.847. 


9. Reduce £2060. 12s. 43d. sterling to Federal mo. 
ney, without premium. Ans. $9158.31. 


EXCHANGE. 199 


10. Reduce £112. 14s. 1d. sterling to Federal money, 


without premium. Ans. $500.91. 
11. Reduce £2. 5s. sterling to Federal money, when 
the premium is 9 per cent. Ans. $10.90. 


12. How much Federal money is equal to £15. 1s. 6d. 


when the premium is 8 per cent. ? Ans. $72.36. 
13. How much Federal money is equal to £80 ster- 
ling, when the premium is 10 per cent. ? 
Ans. $391.11. 
14, How much Federal money is equal to £135 15s. 
10d. English money, when the premium is 8 per cent. ? 
Ans. $651.80. 
15. Reduce £45 13s. 9d. English money to Federal, 
when the premium is 8 per cent. Ans. $219.30. 


16. What will £316 11s. 2d. British money come to 
in Federal money, when the premium is 9 per cent. ? 
Ans. $1533.55. 


17. Reduce £439 16s. 7d. sterling to Federal spy 


when the premium is 84 per cent. Ans. $ 
18. Reduce £2166 16s. 8d. sterling to Federal peurys 
when the advance is 82 per cent. Ans. 


19. Reduce £15656 19s. 14. sterling to Federal mo- 
ney, when the advance is 94 per cent. 


Ans. $ 
20. Reduce 17s. 6d. sterling to Federal money, when 
the advance is 8} per cent. Ans. $ 


21. A merchant in Liverpool sold 200 barrels of flour 
at £2 10s. per barrel; how much Federal money will 
that be, exchange 9 per cent. premium ? 

Ans. $2422.22. 

22. A cotton broker sent to London 70 bales of cot 
ton, each 867 lb.; it was sold at 10d. per Ib. ; ; for how 
much Federal money was it sold, premium 9 per cent., 
and what was his commission at 5 per cent. ? 

Wee $12250.389, 
* ) $612.52 commission. 


= 


200 EXCHANGE. 


23. Shipped to Liverpool, 2000 barrels of flour, which 
cost in New York $4.50 per barrel; it was sold at £1 
18s. 6d. per barrel, when the premium was 8! per cent. ; 
how much was the gain ? Ans. $9565.55. 


24. A grain dealer bought 10 000 bushels of corn, at 
383 cts. a bushel. He sent it to London, where it 
brought 28s. 9d. a quarter, when the premium was 9} 
per cent. ; the cost of transportation was 121 cts. per 
bushel ; how much was Seta 2 Ans. $3657.29. 


25. If 14 bu. 3 pk. 5 qt. are sold at £2 10s. 6d. per 
bushel; how many dollars Federal money will that be, 
exchange 8? per cent. advance? Ans. £ 


26. How much Federal money will pay for 135 ewt. 


3 qr. 14 Ib. of sugar, at 35s, sterling per cwt., premium 
104 per cent. ? Ans. $1167. 90. 


27. A person in Boston received £1000 sterling, from 
England, when the premium was 9 per cent. He put it 
out at interest for 9 mo. 18 da. at 6 per cent. per annum ; 
to how much did it amount ? Ans. $5076.98. 


28. If£459 18s. sterling is put at interest for one year, 
at 5 per cent. per annum, when the pr emium is 8 per 
cent., to how much Feder al money will it amount? 

Ans. $2317.90. 


29. There were sent from Louisiana to England 420 
hhd. of sugar, each 1250 1b.; the tare was 5 per cent. ; 
the sugar sold at Sd. a pound, when the rate of exchange 
was 9 per cent; what was the amount in Federal money ? 

Ans, $80538.89. 


30. Reduce 25000 franes to dollars, at 5 franes 15 
centimes to the dollar. Ans. $4854.88, 


31. A person received from Paris a bill of exchange 
for 52000 francs, 18% cts. to the franc. He put it at 
interest for 8 mo. at 97 per cent. per annum; to how 
much did it amount ? Ans. $9735.44, 


32. How much Federal money in 695 guineas, when 
the premium is 84 per cent. ? Ans, $8519.02, 


EXCHANGE. 201 


33. How many francs 183 cts. each, will it take to pay 
£1054 9s. 41d., when the premium is 91 per cent. ? 
Ans. 27526.99+ frances. 
34, What is the value, in Federal money, of £1 
sterling, when the premium is 9 per cent. ? 
Ans. $4.844. 


35, What is the value, in Federal money, of £1 
sterling, when the premium is & per cent. ? 
Ans. $4.80. 
36. Reduce £1, English money, to Federal money, 
when the rate of exchange is 10 per cent. 
: Ans. $4.885. 
37. Reduce £1 sterling, to Federal money, when the 
exchange is 7 per cent. advance. Ans. $4.752. 


38. What is the value, in Federal money, of £1 


sterling, when the advance is 7 per cent. ? 
Ans. $4.77. 


39. What is the value, in Federal money, of £1 
sterling, when the premium is 83 per cent. ? 


Ans. $4,834. 


Art. 236. To reduce Federal money to English, or 


sterling money, 


Ruie.— Divide the given amount in Federal money, by 
the value of £1 sterling. 


40. Reduce $100, to sterling money, when the ex- 
change is 8 per cent. premium. 


Ans. £20 16s, 8d. 
4}. Reduce $725.50, to sterling money, when the rate 
of exchange is 8 per cent. 
Ans. £151 2s. 11d. 
42. What is the value in sterling money, of $150, 
when the rate of exchange is 9 per cent. 2 
. : Ans. £30 19s. 3d, 


202 PROPORTION, 


43. What is the value in sterling money, of $3500, 
when the premium is 8} per cent. ? 
Ans. £725 16s. 14d. 


44, How much English money is equivalent to 
$864.20, when the premium is 8? per cent. ? 
Ans. £178 16s. 


45, When the premium on sterling money is 94 per 
cent., what is the value of $1.25 2 Ans. 5s. 14d. 


46. When the premium on sterling money is 7 per 
cent., what is the value of $14286.75 ? 
Ans, £3004 4s. 53d. 


47. A person who was going from New York to 
Liverpool, exchanged $2400, to English money, when 
the premium was 8 per cent. How many pounds did 
he get? Ans. £500. 


48. A merchant bought 400 barrels of flour at $104 
per barrel ; he sent the whole to London, where it sold 
at an advance of 20 per cent., when the exchange was 10 
per cent. ; how much did he gain in sterling money ? 

Ans. £859 1s. 93d. 


PROPORTION. 


Art. 237, What is a Ratio 2 


Ratio is the quotient that is produced by dividing one 
quantity by another of the same kind. 

Art. 238. What is a proportion ? 

A proportion is two or more equal ratios. 

Arr. 239. Of how many terms does the rule of pro- 
portion consist ? 


Li consists of four terms; three of which are always 
gruen, and the fourth is to be found from the three terms 
given. 


PROPORTION, 203 
Art. 240. What separate the different terms of a dake 
portion ? 


Two points, thus, :, separate the first and second terms ; 
four points, thus, ::, the second and third ; and two, thus, 
2. the third and fourth, 


Art. 241. What is the meaning of these points 2 


The two denote division, and the four denote equality ; 
that 2s, the quotient of the first term divided by the second, 
as equal to the quotient of the third divided by the fourth. 


Art. 242, What are the first and fourth terms called ? 
Extremes. 


Art. 243, What are the second and third terms call- 
ed 2 


Means. 
Art. 244. What are the first and third terms called ? 
Antecedents, 


Arr. 245. What are the second and fourth terms call- 
ed ? 


Consequents. 


Art. 246. What are the two methods of proving the 
correctness of a proportion ? 


Ist. If the product of the extremes is equal to the pro- 
duct of the means, the proportion is correct. 


Qd. If the quotient of the first term by the second is 
equal to the quotient of the third by the fourth, the propor- 
tion 7s correct. 


Art. 247. To supply any one term of a proportion, 
when three terms are known, 


Ruix.—ZJ/f it be a mean, divide the product of the ex. 


204. PROPORTION, 


tremes by the known mean ; if it be an extreme, divide the 
product of the means by the known extreme. 


Art. 248. To state a sum in proportion, 


Ruis.—Make that quantity which is of the same name 
or kind as the answer, the third term; then consider from 
the other two given terms, whether the fourth term or an- 
swer is to be more or less than the third term; if more, 
place the greater of the other two given terms in the second 
place, and the remaining one in the first; if less, place 
the smaller of the other two given terms in the second place, 
and the remaining one in the jirst. 


Art. 249. To find the fourth term, or answer, after 
the statement is made, 


Rutz.— Reduce the Jirst and second terms to the same 
denomination, and the third term to a_ single denomina- 
tion ; then multiply the second and third terms together, 
and divide ther product by the jirst term; the quotient 
will be the fourth term or answer, and will be of the same 
denomination as the third term, or that to which the third 
term was reduced, 


Note.—To read a proportion, like 7: 14::3: 6, say, as 7 is to 14, sois 3° 
to 6. 


Is 2:4::8:16 acorrect proportion ? 

Is 8:2::6: 4 a correct proportion ? 

Is 5:11: : 64: 133 a correct proportion ? 

Is 6: 16::8: 18 a correct proportion ? 

Is 12 : 20:: 13: 21 a correct proportion ? 

. Is 16:12: : 88: 66 a correct proportion ? 

Is ‘758 : 545: : 14: 6 a correct proportion ? 

. Is 8120: 17180: : 13 : 72 a correct proportion ? 
9. Supply the 4th term in 4:8:: 32: 

10. Supply the Ist term in — : 75: : 25: 10. 


OArAT PO DW 


PROPORTION, 205 . 


11. Supply the 2d term in 15: —:: 45: 120. 


12. Supply the 3d term in 402 ai Gaees —— "281. 
‘13. If 2 lb. of coffee cost 386 cents, what will 14 Ibs. 
cost 2 Ans. $2.52. 
14, If 3 lb. of butter cost 54 cents, what will 2 Ib. 
cost ? Ans, 36 cents. 
15. If '7 bushels of wheat cost $6.20, what will 42 
bushels cost ? Ans. $37.20. 
16. If 12 acres of land cost $726, what will 38 acres 
cost 2 Ans, $2299. 
17. If 29 barrels of flour cost $68.97, what will 43} 
barreld of flour cost ? Ans. $108.454. 
18. If 80 tons of iron cost $650, what will 12 T. 10 
cwt. cost ? | Ans. $270.83£. 
19. If 28 barrels of cider cost $140, what will 14 bar- 
rels cost ? Ans. $7.50. 
20. If 17 gallons of oil cost £8 15s. what will 424 
gallons cost? Ans. £21 17s. 6d. 
21. If 100 lb. of butter cost £10, what will one 
pound cost 2 Ans, 2 shillings. 


22. If a ship can sail 812 miles in one day, how far 
will it sail in 124 days, supposing it sails at the same 


rate ? Ans. 8900 m. 
23. If 25 square yards of oil cloth cost £7 10s., what 
will 142 square yards cost ? Ans, £4 8s. 6d. 


24. If you can buy 13 cords of wood for $84.50, how 
many cords can you buy for $21.12} 2 
: Ans. 34 cords, 


25. How many feet of lumber can be bought for 
$78.50, at the rate of $25 per thousand ? 
Ans. 3140 feet. 


26. If a horse can run 40’ of a circle in 3 seconds, 
how long will it take him to run the whole circle ? 
Ans, 27 min. of time. 
18 


206 PROPORTION. 


27. If 4 bu. 3 pk. cost $10.50, what will 75 bushels 


cost ? Ans. $165.78+6§. 
28. If 12 lb. 8 oz. of gold cost $2400, what will 21 
ounces cost ? Ans. $842.853. 


29. If 31 cwt. 1 qr. 14 lb. of sugar cost $318.45, 
what will be the price of a hogshead that weighs 1240 
pounds ? Ans. $125.80. 


30. If12 A. 3 R. 28 sq. p. of land cost $2460, how many 
acres can be bought for $10 000 ? 
Ans, 52 A. 2 R. 6 sq. p. 153%); sq. yd. 


31. 850 men have provision enough to last 4 mo. 15 
days; how long would the same provisions last 240 
men ? Ans. 6 mo. 16% days. 


32. If you can buy 44 gross of pens for £53 12s., how 
many gross can be bought for £12 18s. 6d. ? 
Ans. 10227 gross. 


33. If it take 20 men 112 days to dig a sewer, how 
long will it take 48 men to dig the same sewer ? 
Ans. 462 da. 


34. A corn merchant sent 1400 bushels of corn to 
London and sold them for £210; he afterwards sent 
10500 bushels, and received the same price per bushel ; 
for how much did he sell the second lot of corn ? 

Ans. £1575. 


35. If 387 bushels cost $112.874, how many bushels 
can be bought for $300 ? 
Ans. 98 bu. 1 pk. 2234 qt. 


36. If 33 gallons of molasses cost 80 cents, how many 
hogsheads can be bought for $3120.80 ? 
Ans. 20822 hhd. 


37. If 34 men can build a house in 40 days, how long 
will it take 12 men to build the same house? 
Ans. 1132 days. 


38. A farmer can plough 3 reods and 12 square rods 


PROPORTION. 207 


of land in 1 day ; how long will it take him to plough 5 


acres ? Ans. 62; days. 
39. If 424 tons of coal cost $206.20, what will be the 
price of 14 tons 3 Ans. $8.4944,. 


40. If $172 will buy provisions to .ast 8 months, how 
much will it take to buy provisions for 18 months ? 
Ans. $39.933, 


41. If a man perform a piece of work in 20 days, 
when he works 10 hours per day, how long will it take, 
if he works 12 hours a day ? Ans. 16% days. 


42. If 24 yd. 3 qr. of carpet, which is one yard wide, 
will cover a room, how long must the carpet be, that is 
12 yards wide, to cover the same room ? 

Ans. 144 yd. 


43. If 18% bags of coffee contain 7581 pounds, how 
many pounds will 800 bags contain ? 
Ans. 12136 Ib. 


44. How long will it take a person to travel 1290 
miles, at the rate of 8063 miles in 20} days? 
Ans, 8636 days. 
45. If 172 cords of wood cost $883, what will 2543 
cubic feet cost ? Ans. $9.95. 


46. If 38,3, ewt. of tobacco cost $1142, what will 13 
tons 154 cwt. cost ? Ans. $822.90. 


47. If 432 cords of wood cost £92 12%s., how many 
cords can be bought for £632? Ans. 29¢. 121 cu. ft. 


48. If 775 barrels cost $31}, what will 322 barrels 
cost ? Ans. $182. 


49. If 2 bu. 1 pk. of wheat cost $1.932, how many 
bushels can be bought for $9622 Ans. 1122 bushels. 


50. If it cost $1.384 per square foot to pave a floor 
382 feet long by 25 feet wide, what will it cost to pavea 
floor 31 feet long by 224 feet wide? 

Ans. $966.04, 


208 PROPORTION. 


51. What will it cost to pave a floor 493 feet by 274 
feet wide, at $1.45 per square foot? Ans. 


52. If 18 men can build a house in 80.75 days, how 


long would it take 82 men ? Ans. 
53. If 44.3 square yards cost $72.25, what will be the 
price of 87.09 yards ? Ans. 


54. If one bottle holds 1.875 pints, how many bottles 
will it take to hold 2.5 hhd. ? Ans. 


55. If 174 bushels cost £8.75, what will 800.16 bushels 
cost ? Ans. 
56. If 1425.6 bags of coffee, each bag weighing 62.5 
pounds, cost $12080, what will 718.75 pounds cost ? 
Ans. 


57. If 456 barrels beef last a garrison for 662 days, 
how long will 89.4375 barrels last them ? 
Ans. 15 days. _ 


58. Ifa man can walk 89.4875 miles in 4} days, how 
many miles can he walk in 43.4,%5 days? 


Ans. 


59. A person has a sum of money at interest, which 
yields $560, at the rate of 7 per cent. per annum ; what 
rate per cent. per annum must he charge, so as to receive 
$1000 2 Ans. 124 per cent. 

60. $6400 put at interest for 1 year at the rate of 74 
per cent. per annum, yields $480; at what rate per cent. 
per annum must $9000 be put at interest, so as to yield 
the same sum ? Ans. 52 per cent. 

61. If 14 men can be boarded for 1 week for $45.50, 
what will it cost to board 5 men and 4 women, for one 
week; the women being boarded at half price ? 

Ans. $22.75. 

62. If 75 tons of iron cost $5400, what will 35 T, 16 
ewt. 1] qr. 14 lb. cost ? Ans. 

63. If 18 T. 11 ewt. 1 qr. 22 lb. of iron cost $880, 
what will 5 tons cost ? Ans, 


COMPOUND PROPORTION. 209 


64. If 17 tons of iron cost $1224, how many tons 
may be bought for $3811.50 ? Ans. 


65. What will 800 barrels of pork cost, at the rate of 
114 cents a pound, counting 200 lb. to the barrel ? 


Ans. 
66. What will be the cost of 38311 feet of bourds at 
£7 16s. per 1000 feet ? Ans. 


67. What will be the cost, in Federal money, of 369 
yd. 3 qr., at 3s. Yd. New York currency for 2} yards? 
| Ans. 69.33. 
68. What will be the cost, in Federal money, of 386 
bu. 1 pk. 4 qt. of barley, at £1 11s. 6d. sterling, for 5 bu. 
2 pk., exchange 9 per cent. ? Ans. $536.01. 
69. What will a piece of French cloth, 484+ metres 
long, cost at £1 10s. sterling, a yard; the metre being 
counted 175 yd., and the premium 8 per cent. ? 
Ans. $337.35. 
70. How many yards of cloth may be bought for 
£150 sterling, premium 10 per cent., at the rate of 
$18.24 for 5 yards ? Ans. 201747 yd. 
71. How many yards of cloth may be bought for 
$398.60, at the rate of £5 11s. 8d. sterling, for 3} yards, 
exchange 9 per cent. ? Ans. 51 yd. 2 qr. 1 na. 


CON OUND PRO Ob CLG Ns 


Art. 250. What is Compound Proportion ? 


A compound proportion is a combination of two or more 
proportions. 


Art. 251. To state a sum in compound proportion, 


lst. Place that quantity in third term which is of the 
same name or kind us the answer ; 
2d. Take any two of the remaining terms that are of 
the same name or kind and determine from them, whether 
18* 


210 PROPORTION. 


the answer will be more or less than the third term, and 
place them in the form of a ratio, as directed in simple 
proportion ; then take other two like terms and arrange 
them as a second ratio under the first; so proceed till all 
the terms are employed, 


Art. 252. To find the fourth term, 


Ru.rt.—Reduce the third term to one denomination, and 
af the two terms of any ratio be of different denominations, 
reduce them to the same ; then multiply the third term and 
all the second terms together, and divide this product by 
the product of all the first terms ; the quotient will be the 
answer, Or, 


When the terms are all reduced, form a sum in simple 
proportion by taking the first ratio and the third term ; make 
the fourth term thus found, a third term to the second 
ratio, and from this find a fourth, and so proceed to the 
last ratio, when the fourth term will be the answer. 


Notr.—If the operations to be performed are indicated, by using the signs of 
yeultiplication and division, the work can often be abbreviated by canceling. 


1. If it cost $40 to board 3 men for 5 weeks, what 
will it cost 12 men to board for 10 weeks ? 
Ans. $820. 


2. If 18 men can consume 34 barrels of provisions in 
135 days, how long will it take 45 men to consume 102 
barrels of provisions ? Ans. 162 days. 


3. What will be the charge for the tuition of 14 boys 
for 184 months, if 12 boys are charged $2000 for one 
year ? Ans. $3597.22 

4, If 120 men can build a 4 mile of wall in 15} days, 


how many men would it require to build a wall 352 
yards long, in 402 days ? Ans, 18 men. 


5. If 200 men can build 125 rods of railroad in 30 
days, how many men would it require to build 25 miles 
in 80 days ? Ans, 4800 men. 


COMPOUND PROPORTION. 211 


6. If 13 men can earn £63 13s. in 3} weeks, how 
much will 89 men earn in 212 days, counting 6 days to 
a week ? Ans. £2159. 


7. If a load containing 18 ewt. 50 lb., be carried 54 
miles for $7.20, what will be the charge for carrying 112 
I. 15 ewt. 624 miles ? Ans, $9972.97. 


8. If the board of 64 persons for 13 weeks is $2704, 
what will it cost to board 19 men 54 weeks ? 
Ans. $339.625. 


9. If 75 horses eat 52 tons of hay in 74 weeks, how 
much will 40 horses eat in 140 days ? 
Ans. 54 tons. 


10. If 6 apprentices can earn £75 12s. in 274 weeks, 
by working 2 hoursa day at overwork, how much could 
15 apprentices earn in 414 weeks, working 14 hours a 
day at overwors ? Ans, £212 12s, 6d. 


11. When flour is $6.50 per barrel the ten cent loaf 
weighs 2.125 pounds, how much will the 5 cent loaf 
weigh when flour is $7.25 per barrel ? 

Ans. 323 |b. 

12. If it cost $2.3874 to paint a surface 15 feet long 
and 133 feet wide, how much will it cost to paint a sur- 
face 250 feet long and 103 feet broad ? 

Ans, $31.97. 


18. If the interest of $6.50 for 3 yr. 103 mo. be $104. 
15, what will be the interest of $445,624 for 7 years ? 
Ans. $128.99. 


14. If 20 men, working 11 hours a day for 35 days, 
can earn $3250, how much can 86 men earn in 48 days, 
working 104 hours a day ? Ans. $6860.45. 


15. If 10 can mow 143 acres in 44 days, by working 
84 hours per day, how many men can mow 20 acres in 
52 days, working 32 hours per day? Ans, 27 men. 

16. If 20 men, working 10 hours a day for 38.5 days, 
build a wall 90 feet long, 6 feet high, 4 feet thick, how 


212 PRACTICE. 


long will it take 75 men to build a wall 325 feet long, 
4,2; feet high, and 3} feet thick, working 11 hoursa day ? 
Ans. 18 2 days. 


PRACTICE: 
Art. 253. What is Practice ? 


Practice is a method of finding the value of various ar- 
ticles by means of aliquot parts of a unit whose value is 
given. 


Arr. 254, What are aliquot parts ? 


They are parts that always have a unit in the numera: 
tors, and a whole number in the denominator. 


TABLE OF ALIQUOT PARTS. 


an) 
bo|= 


50 cents = 4s. 
66 


Of rf Cn] J ol — 


tH U th & tH th & th & 


— 
— 


Colt bo] 
ey ee Se) pe 


oN a Ue ll 


| 
ty 


hd Obl C2] pf | 
oS 


\ 


PRACTICE, 213 


Arr. 255. What is the general rule for Practice 2 


Rotr.—Sind the value of the given sum or quantity at 
the rate of some unit of value, asa shilling, pound, or 
dollar, dc. ; then multiply this value by as many shil- 
lings, pounds, or dollars, dc., as there are in the price of a 
unit whose value is given, and separate the residue into 
aliquot parts of a shilling, pound, or dollar, &c., and find 
the value accordingly ; add the several results, and their 
sum will be the total value, If the given sum or quantity 
consist of several denominations, multiply the value of a 
unit by as many as there are of those units, and separate 
the smaller denominations into aliquot parts of some higher 
whose value is known, and add as before. 

NotEe.—When the price is separated into aliquot parts, the answer will be 
of the same denomination as the unit of which aliquot parts were first taken ; 


otherwise it will be of the same denomination as that of the unit whose va- 
lue is given. 


1. How much wil! 725 bushels of rye cost at 25 cents 


a bushel ? Ans. $181.25. 

2. What will be the price of 1866 pounds of coffee at 
162 cents a pound ? Ans. $311. 

3. What is the cost of 1951 gallons of oil at $1.334 
a gallon ? Ans. 2601.334. 


4, What is the value of a hogshead of sugar, weigh 
ing 1505 pounds, at 83 cents a pound? 
Ans, $125.42. 


5. What will be the value of 759 yards of cloth at 


_ $4.75 a yard 2 | Ans, $ 
6. What cost 987 pounds of tea at 824 cents a pound ? 
( Ans. $ 
7. What is the price of 1500 bushels of corn at 934 
cent a bushel ? Ans. $ 
8. How much will 1683 yards of muslin cost at 814” 
cents a yard ? Ans. $ 


9. What cost 1896 yards of muslin at 912 cents a 
yard ?- Ans, &. 


214 PRACTICE. 


10. How many dollars will 225 pounds of coffee cost 


at 1s. 4d. a pound ? Ans. $37.50. 
11. How many dollars will 866 yards of muslin cost 
at 2s. Sd. a yard ? Ans. $288.662. 
12. Find how many dollars 361 pounds of tea will 
cost at 5s. 4d. a pound. Ans. $ 
13. What will be the price, in dollars, of 791 gallons 
of oil, at 6s. 8d. a gallon ? Ans. $ 
14. How many dollars will 3000 bushels of corn cost, 
at 5s. 84d. a bushel ? Ans. $ 
15. What is the value of 100 pounds of sugar at 6 
pence a pound ? Ans. £2 10s. 
16. What is the value of 250 pounds of sugar at 4 
pence a pound ? Ans. £4 13s. 4d. 
17. What is the value of 306 pounds of coffee at 9 
pence a pound ? Ans. £11 9s. 6d. 
18. What is the value of 1575 pounds of beef at 11 
pence a pound? , Ans. £72 3s. Od. 
19. What is the value of 2839 yards of muslin at 4} 
pence a yard ? Ans. £53 4s. Td$. 
20. What is the value of 2354 yards of muslin at 74 
pence a yard ? Ans. £73 11s. 3d. 
21. What is the value of 8967 yards of calico at 8} 
pence a yard ? Ans. £136 7s, 3d. 3qr. 
22. What is the value of 5888 yards of gingham at 
10? pence a yard ? Ans. £263 14s. 8d. 
23. What is the value of 6859 pounds of tea at 113 
pence a pound ? Ans. £335 16s. 14d. 
24. What is the value of 98655 yards of muslin at 1s. 
Sd. a yard ? Ans. £8221 5s. 


25. What is the value of 16798 yards of muslin at 2s. 
5d. a yard? Ans, £2029 15s. 2d. 


os 


PRACTICE. 215 


26. What is the value of 5699 pounds of cloves at 4 


shillings a pound ? Ans. £1189 16s. 
27. What is the value of 3486 yards of cloth at 15 
shillings a yard ? Ans, £2614 10s. 
28. What is the value of 7961 yards of cloth at 17 
shillings a yard ? : Ans. £6766 17s. 
29. What is the value of 6875 yards of cloth at 19 
shillings a yard ? Ans. £6531 5s. 
30. What is the value of 9675 yards of satin at 12s. 
6d. a yard 2% Ans. £6046 17s. 6d. 
31. What is the value of 9110 yards of silk at 13s. 
4d. a yard? Ans. £6073 6s. 8d. 
32. What is the value of 7568 yards of silk at 16s. 
Sd. a yard? Ans. £6306 13s. 4d. 
33. What is the value of 16998 yards of silk at 18s. 
4d. a yard? Ans. £15581 10s. 
34. What is the value of 5386 boxes of oranges at 
15s. 94d. a box 2 Ans. £4252 13s. 11d. 
35. What is the value of 7129 boxes of raisins at 17s. 
63d. a box? Ans. £6260 3s. 02d. 
36. What is the value of 18659 bushels of potatoes 
at 14s. 114d. a bushel ? Ans. £13955 7s. 63. 
37. What is the value of 6759 bushels of corn at 18s. 
83d. a bushel ? Ans. £6829 10s. 51d. 
38. What is the value of 7667 pieces of ribbon at 19s. 
53d. a piece? Ans. £7467 6s. 91d. 
39. What is the value of 681 pieces of cloth at £1 
13s. 4d. a piece ? Ans, £1135. 
40. What is the value of 9561 pieces of bombazine at 
£2 10s. 4d. a piece ? Ans, £24061 17s. 
41. What is the value of 5671 pieces of satin at £3 
9s. Sd. a piece ? Ans, £19753 19s. 8d. 


42. What is the value of 4756 pieces of cloth at £5 
16s. 7d. a piece ? Ans. £27723 10s, 4d. 


216 PRACTICE. 


43. What is the value of 987 pieces of clothat £4 


15s. 3d. a piece ? Ans. £4700 11s. 9d. 
44, What is the value of 398 pieces of silk at £8 13s. 
93d. a piece ? Ans. £3458 9s. 1d. 
45, What is the value of 886 pieces of silk at £9 6s. 
Tid. a piece ? Ans, £8266 11s. 34d. 
44, What is the value of 1921 boxes of citron at £7 
11s. 53d. a box ? Ans. £14547 11s, 54d. 
47. What is the value of 5 cwt. 2 qr. 123 lb. of sugar, 
at $7.50 a cwt. ? Ans. $42,183. 
48. What is the value of 18 cwt. 3 qr. 124 lb. of sugar, 
at $6.80 a cwt. ? Ans. $128.35. 
49, What is the value of 21 cwt. 1 qr. 18 Ib. of to- 
bacco, at $8.75 a cwt. ? Ans. $187.5125. 
50. What is the value of 17 T. 15 ewt. 2 qr. 124 Ib. of 
iron, at $75 a ton? Ans. $1333.593. 
51. What is the value of 26 T. 18 cwt. 3 qr. 22 lb. of 
copper, at $245.20 a ton ? Ans. $6607.7625. 
52. What is the value of 17 cwt. 2 qr. 17 Ib. of iron, 
at $84.75 a ton ? Ans. $74.876+. 
53. What is the value of 18 ewt. 1 qr. 24 lb. of cheese, 
at $225 a ton ? Ans. $151.77 
54 What is the value of 71 A. 2 R. 15 sq. p., at 
$325.50 an acre ? Ans. 
55. What is the value of 615 A. 3 R. 32 sq. p., at 
$164.80 an acre ? Ans. 
56. What is the value of 28 Ib. 7 oz. 16 dwt. of silver, 
at $13.50 a pound ? Ans, 


57. What is the value of 43 bu. 2 ite 7 qt. of corn, 
at 58 cts. a bushel ? Ans 


5&8. What is the value of 19 hhd. 28 gal. 3 qt, of 
molasses, at $28.30 a hhd, ? Ans. 


CUSTOM-HOUSE BUSINESS. D1, 


59. What is the value of 16 cwt. 2 qr. 10 lb. of sugar, 
at $5 a cwt. ? ee ha ak 


60. What is the value of 41 ewt. 3 qr. 17 1b. of iron, 
at £25 a ton? Ans. £52 83. 


61. What is the value of 837 A. 3 R. 15 sq. p., at £47 
an acre ? £1778 13s. 15d. 


62. What is the value of 12 lb. 10 oz. 14 dwt. of 
gold, at £63 12s, a pound ? Ans. £819 18s. 2.4d. 


63. What is the value of 15 yd. 3 qr. 3 na. of cioth, 
at £1 17s. a yard? Ans. £29 9s, 844d. 


s 


CUSTOM-HOUSE BUSINESS. 


Arr. 256. What is Gross Weight ? 


Gross weight is the total weight of any article, together 
with the hoyshead, box, or bag, &c. 


Art. 257. What is tare ? 


Tare ts an allowance made for the weight of the hogs- 
head, box, or bag, &c., in which merchandise is transported 
From 6ne place to another. 


Art. 258. What is draft or tret 2 


It is an allowance made for waste or impurities, leak 
age, &e. , 


Arr. 259. What is net weight ? | 
Net weight is the actual weight of the article itself. 
Arr. 260. To find the net weight, 


Ruie.—First deduct the draft or tret, and from the 
remainder subtract the tare; this remainder will be the net 
weight. 


1, A merchant bought a hogshead of sugar which 
19 


218 CUSTOM-HOUSE BUSINESS. 


weighed 1350 pounds: the tare was 13 pounds; what 
was the net weight ? Ans. 1837 pounds. 


2. Bought 14 hogsheads of sugar weighing 1250 
pounds each; if the tare is 15 pounds a hogshead, what 
is the net weight of the whole? Ans, 17290 lb. 


3. A grocer bought 100 tierces of rice, each weighing 
250 pounds; what is the net weight, the tare being 5 per 
cent. ? Ans. 23750 Ib. 


4, “A tobacconist bought 12 hogsheads of tobacco, each 
weighing 15 cwt. 2 qr. 11 1b., tare 50 pounds per hogs- 
head ; what was the net weight ? Ans. 18132 lb. 


5. Bought 250 bags of coffee, each bag 73 Ib., tare 4 
per cent. ; what was the net weight? Ans. 17520 Ib. 


6. What is the price of 45 hhd. of sugar, each weigh- 
ing 12 cwt. 0 qr. 15 lb., at 82 cts. per pound; tare 7 per 
cent. ? Ans. $4449.178+. 


7. What is the price of 5 casks of wine, marked as 
follows :— 


Ist. cask 148 gallons. 
2d. “ 158 . 
daw 3 anlD2avas 
4th “ 145 “ 
Sth ate 0 Ne 
The leakage is 2 per cent., and the price $2} per gal- 
lon? Ans. $1647.135. 
8. A grocer bought 5 hhd. of sugar, each averaging 
13 cwt. 1 qr. 12 lb., at 74 cts. a pound; the draft was 
14 lb. per ewt., and the tare 5 per cent.; what is the 
price of the net weight ? Ans. $469. 165+. 


9. Received from Rio Janeiro, an invoice of 450 bags 
of coffee, averaging 76 lb. per bag. The tare was 8 per 
cent., and the invoice price 102 cts. per lb. -If the 
coffee is sold at a profit of 332 per cent., what will be the 
selling price per pound, and how much will be the total 
profit 2 iN 14 cts. 

$1161.09 total gain, 


DUTIES. 219 


10. A grocer bought at auction, 4 hhd. of sugar, each 
weighing 11 ewt. 2 qr. 20 Ib. The tare was 124 per 
—cent., what was the price of the net weight at 8} va per 
lb. ? | Ans, $348.08. 

A sugar refiner bought 5 hhd. of Louisiana sugar, 
Ww ane as follows: Ist. , ll cwt. 1 qr. 14 Ib., tare 23. Ib, 
5 Re Be cwt. 0 qr. 16 1b., tare 25 Ib. od., 10 ewt. 3 qr. 
21 ‘lb., tare 22 Ib. 4th., 12 cwt., tare 24 Ib, 5th., 13 
swt, 1 qr. 12 lb., tare 26 lb. What was the price of the 
et weight, at $9.50 per cwt. ? Ans. $557.46. 

12. A grocer bought 6 cases of sugar, weighing as fol 
lows: the Ist., 5 cwt. 3 qr. 15 Ib. 2d., 6 cwt. 1 qr- 
3d., 5cewt.2qr.14]b. 4th., 4 ewt. 3 qr. 20 lb.  5th., 
7 ewt., and the 6th.,5 ewt. 1 qr. 71b. The tare was 15 
Ib. per cwt. What was the price of the net weight at $8 
per cwt. ? Ans. $238.408. 


——s 


DUTIES. 


Art. 261. What are Duties 2? 


Duties are certain amounts levied by government on ar 
ticles imported, for the purpose of defraying its expenses, 


Art. 262, How many kinds of duties are there ? 
Two: specific and ad valorem duties. 
Art. 263, What is a specific duty ? 


It is a duty imposed on articles according to their weight 
or measure, without regard to cost. 


Arr. 264,. What is ad valorem duty ? 


It is a duty imposed on articles according to their value, 
and is generally reckoned by percentage. 


NoTE. —Specific duty is imposed on the net weight; ad valorem duty, on 
the invoice, without any deductions whatever. 


220 CUSTOM-HOUSE BUSINESS. 


13. Received from Lyons, 1 case of silks, contaiting 
75 pieces, averaging 314 yards to the piece, and invoiced 
at 88 cents per yard; what is the duty at 103 per cent. ? 

Ans. $218.29. 


14, A merchant received from England 250 pieces of 
broadcloth, worth $3.50 per yd.; if each piece measure 
534 yd., what will be the duty at 30 yer cent. ? 

Ans. $13978.18. 


15. A merchant received from Demarara, 167 bags ~ 
of coffee, 172 Ib. per bag, invoiced at 83 cents per Ib. ; 
the tare was 5 per cent. ; what was the duty at 162 per 
cent. 2 Ans. $886.58. 


16. A grocer received fiom Canton 200 chests of tea, 
63 lb. per chest; the tare was 7 per cent.; what was 
the duty at 84 cents per Ib. ? Ans. $996.03. 


17. If l import 80 tons of iron at $78 per ton, duty 
334 per cent., and sundry expenses $2.50 per ton, what 
will the whole cost me ? Ans. $8520. 


18. A merchant imported 45 cases of cotton goods, 
each containing 60 pieces, each piece 38% yards, invoiced 
at 6 cents per yard; what is the duty at 24 per cent. ? 

Ans. $156.94. 


19. A liquor dealer received from Bourdeaux, 17 pipes 
of brandy, marked 114 gallons each, and invoiced at 
$1.75 per gallon. Ifthe leakage be 2 per cent., the du- 
ty equivalent to the value of the brandy, and the other 
charges 14 per cent., what will the whole cost him ? 

Ans. $6697.195+. 


20. What is the duty on 54 T. 13 cwt. 3 qr. 20 1b. of 

iron, invoiced at $45 a ton, and the duty 334 per cent. ? 
Ans. $820.46. 

21. Received from Malaga, 725 boxes of raisins, each 

box weighing 18 |b, invoiced at 62 cents per pound. The 

tare was 2 lb. per box, and the duty 7 per cent.; for 


how much must he sell them to gain $250? 
Ans. $1087.81. 


BARTER. 221 


22. A merchant imported a case of silk plush from 
Mentz, in France. The case contuined 41 pieces, each 
piece 253 metres, at $2 a metre; the duty was 10 per 
cent. ; how much a yard must he sell the plush to gain 
25 per cent, ? Ans: $2.54 (nearly.) 


23. If I import 750 pieces of silk braid, each piece 50 
metres, invoiced at 6 cents per metre, on which there is 
a duty of 15 per cent., how much will I gain by selling 
it at 9 cents per yard ? Ans. $1068.75. 


24. Mesier & Hauptman imported 12 cases German 
cloth, each case containing 34 pieces, averaging 85 aunes 
to the piece, and invoiced at $2.50 the aune. The duty 
was 20 per cent. How much will they gain on a yard 
by selling at an advance of 331 per cent., and what will 
be the duty ? el: 80 cts. a yd. gain. 

* | $7140 duty. 


B AUR DERE 
Art. 265. What is Barter 2 


Barter is the exchange of one kind of produce or mer- 
chandise for another. 


Art. 266. How are sums in Barter calculated 2 
By the rules of analysis. 


1. A person exchanged a watch valued at $80, for po- 
tatoes at $1.25 per bushel; how many bushels did he 
get ? : Ans. 64 bushels. 


2. A gave B a house and lot worth $2500, for 400 
barrels of flour; what was the value of the flour per bar- 
rel ? Ans. $6.25. 


3. How many yards of muslin at 45 cents per yard 
can be bought for 900 bushels of wheat, valued at $1.873 
a bushel ? . Ans. 8750 yards. 

19* 


222 BARTER, 


4. Ifa pound of sugar is worth 74 cents, how many 
pounds can be got for 2 tons 10 cwt. of iron at S60 a 
ton ? Ans. 2000 Ib. 


5. If 45 ewt. 2 gr. 124 Ib. of raisins, at $138.44 per 
ewt., be exchanged for 1022 gallons of alcohol, what will 
be the price per gallon ? Aus. 60 cents. 


6. How many acres of land, at $150 per acre, can be 
exchanged for 7 50 barrels of flour, at $4.60 per barrel ? 
Ans. 23: acres. 


7. A person traded 456 yd. 3 qr. 2na. of broadcloth, 
at $2.50 per yard, for molasses at 25 cents per gallon ; 
how many gallons did he get ? Ans. 45683 gal. 


8. A person exchanged two houses and lots, valued at 
$2500 each, for 15 A. 3 R. 20 p. of land; what was the 
price per acre ? Ans. $314.96. 


9. How many pounds of butter at 25 cts. a pound 
can be exchanged for 74 yd. of cloth valued at $4.50 a 
yard? Ans, 185 |b. 


10. A country pedlar offered a farmer a piece of mus- 
lin which contained 60 yd., for a firkin of butter, valued 
at 224 cts. a pound; how much does the pedlar value 


his muslin a yard 2 Ans. 21 ets. 
11. How many yards of cloth at $4.50, should be 
given for a watch worth $63.90 ? Ans. 141 yd. 


12. At $42 a thousand, how many feet of lumber 
should be given for a farm gontaining 83 A. 2 R. 16 p., 
valued at $250 an acre ? Ans, 200 thousand. 


13. A person had 689 lb. tea, worth 88 cts. a pound, 
which he exchanged for sugar, at 55 cts. a pound ; how 
many pounds of sugar did he get ? Ans, 11024 Ib. 


14. Three persons entered in a partnership, in which 
the first put $4000, the second, $7000, and the third, 
$10000; their profits were 162 per cent., with which 
they pur rchased a farm containing 4.375 acres ; what was 
it worth an acre? Ans. $800, 


BARTER. 293 


15. A merchant had 22 pieces of cloth, each piecs 
measuring 28% yards, which he bartered for 954 tons 
of sugar, at 104 cts.a pound; what was the value of the 
cloth per yard ? 

Ans. $3.00. 

16. 750 barrels of flour were consigned to New York 
from Oswego; they sold for $5} a barrel, commission 
1% per cent. The balance was laid out in white lead, at 
62 cts. a lb., how many pounds of lead were sent to 
Oswego ? Ans. 55876.734-+ lb. 


17. A merchant, has 160 barrels of pork, valued at 
$10.50 a barrel, for cash, but he charges in barter an 
‘advance of 10 per cent. ; he sells 3 of the whole for cash, 
“and exchanges the rest for corn, at 42 cts. a bushel; how 
many bushels does he get ? * Ans. 1100 bushels. 


18. A bought 13 hhd. ofsugar, each weighing 12 ewt. 
1 qr. 16 1b. gross, tare 74 per cent., at 11 cts. per pound 
net ; if he exchange the net at an advance of 5 per cent. 
for potatoes, at $2.38 a barrel, how many barrels will he 
get 2 Ans. 724.2 bar. 


19, A. merchant sent 15000 bushels of grain to Liver- 
pool, which was sold at 255 pence sterling, a bushel, 
when the exchange was 8 per cent. premium; if he 
should receive 1593 yd. 3 qr. of English cloth in pay- 
ment, what would be the value of one yard, in Federal 
money ? Ans. $4.80. 


20. If 34 T. 16 cwt. 1 qr. 5 |b. of copper, at $820 a 
ton, be exchanged for $6000 in money and wine, at $2.25 
a gallon, how many gallons of wine will there be ? 

Ans, 2284.8 gal. 


21. A person put $1600 at interest for 9 months, at 7 
per cent. per annum, and spent the interest for butter, at 
25 cts. per pound; how many firkins of 56 Ib. each, did 
be get? Ans. 6 firkins, 


22. A bought 96 yd. 38 qr. of oil cloth, at $1 per 
yard, which he sold at a profit of 334 per cent., and 


224 PARTNERSHIP. 


invested the proceeds in carpet, at $1.72 a yard; how 
many yards did he get? iE Ans. 75 yd. 


23. Sold 2 hhd. of wine at $2.10 a gallon, and gained 
5 per cent.; spent the profit in muslin at 20 cts. a yard ; 
how many yards were there? Ans. 63 yds. 


—— 


PARTNERSHIP. 
Art. 267. What is Partnership ? 


It is a rule by which, when two or more persons engage 
in business, itis found what share of the gain or loss 
each is to receive or pay. 


Art. 268. How many kinds of partnership are there ? 
Two: simple and compound. 
Art. 269, What is simple partnership ? 


It is when two or more persons transact business, and 
share the gain or loss without regard to time. 


Arr. 270. What is the rule for simple partnership ? 


Ruite.—Find what part of the whole capital, the gain 
or loss is; multiply the resulting fraction by each man’s 
capital separately, and the products will show the gain or 
loss of each. 


1. Two men enter into partnership; the first puts in 
$60, and the second, $80, and they gain $35; to how 
much was each entitled ? ee? $15 for the Ist. 

* {$20 for the 2d. 


2. A and B enter into partnership; A puts in $300, 
and B puts in $200; they make $400;.to how much is 
each entitled ? "Ane $240 for the Ist. 

* ) $160 for the 2d. 


3. Three persons entered into a speculation ; the first 


PARTNERSHIP. 225 


e 
put in $4000, the second, $5000, and the third, $6000 ; 
they lost $2000; what part of the loss must each bear ? 


$533.332. 
Ans. ; $666.66. 
$800. 


4. Three persons opened a store, and stocked it with 
goods to the amount of $13000; the first put in $3500, 
second, $5450, and the third put in the balance ; they 
gained $5600 ; to how much was each entitled ? 


Ans. ! 4 


5. Three men formed a copartnership ; into which the 
first put $3825.20, the second, $4811.50, and the sare 
$9006.30; they gained 25 per cent. of their capital ; 
how much was each entitled 2 

$956.30 for the Ist. 
Ans. 4 $1202.874 for the 2d. 
$1251.574 for the 3d. 

6. A, B, C, and D, ship flour to Liverpool; A fur- 
nishes 600 barrels, B, 450 barrels, C, 780 barrels, and 
D, 1112 barrels; during a storm 650 barrels were 
thrown overboard; what portion of the loss must each 


share ? | 1 32528. A’s share, 
( Boe jae Je 66 
TAC eat ee 


7. Three men hired a pasture ground for cattle for one 
year, at an expense of $45; the first has 100 head of 
cattle in pasture, the second, 150, and the third, 50; how 
much must each pay ? $15. 
Ans. < $22.50 

$7.50 


8. X, Y, and Z gained in one year $1566.75; X put 
n $3150, Y, $5000, and Z, $4560; what is the share of 
zach, i for ix. 
Ans. for Y. 

for Z, 


226 PARTNERSHIP. 


9 
9, A and B entered into a speculation and gained 
$2000; A advanced $3000, and B $2000; what per cent. 
was gained ? Ans. 40 per cent. 


10. Smith, Jones, and Brown enter into partnership, 
and make $1650; Smith put in $5600, Brown, $4900, 
and Jones, $8500; to how much of the gain was each 
entitled ? $660 for Smith. 

Ans. 4 $577.50 for Jones. 
$412.50 for Brown. 


11. A vessel got aground; in order to lighten her, 
the captain ordered 200 barrels of flour that belonged 
to X, and 40 barrels that belonged to Y, to be thrown 
overboard ; X lost 4 of his shipment, and Y, 2 of his; 
how much was the shipment of each? 

) ne 
Ans. Y. 

12, A and B entered into trade; A put in $5000 and 
B 800 barrels of flour; they gained $1800, of which B 
took $800 for his share of the gain; how much was B’s 
flour per barrel ? Ans. $5 per barrel. 


13. Smith and Brown opened a grocery; Smith put 
in 800 firkins of butter, each firkin 56 lb., at 204 cents 
per pound, and $1000 in cash; Brown put in $3000; 
they gained $2010.12; what was the share of each? 

hae § $1200.02 Smith. 
"($810.10 Brown. 


14. Brown & White enter into a partnership in the 
dry good business; Brown puts in 100 pieces of cloth, 
each piece 28% yards, at $2.50 per yard; 150 pieces of 
linen, each piece 12 yards, at '75 cents a yard, and $500 
in cash ; White puts in 350 pieces of muslin, each piece 
32 yards, at 237 cents per yard, and $2000 cash; they 
lost $2800; how much of the loss must each sustain 2 

A owes Brown, 
"| $782.48 White. 


15, A and B started a cotton factory ; A fitted up the 


PARTNERSHIP. D7 


puilding with machinery, &c., to the value of $8500; B 
furnished the raw material worth $12650; they gained 
$5562.50 ; what was the share of each ? 
ie Witenes Ik 
" ) $3326.98 B. 


16. Three persons, A, B, and C, built a sloop, A fur- 
nished $1000, B $1200, and C 20000 feet of lumber ; 
they gained in one year $5400, of which C was entitled 
to $1000; what were the profits of A and B, and the 
, price per 1000 feet of C’s lumber? 

$2000 for A. 
Ars. | $2400 for B. 
$25 for 1000 ft. of C’s lumber. 


A, B, and C commence business; A puts in 250 
fvking of J butter, B puts in $2500, and C $4100; their 
profits amounted to $2210, of which A took $560 ; how ° 
much was his butter a pound, and to how much were B 
aud C entitled ? 16 cents a pound for C’s butter. 

| $625 for B. 
} $1025 for C. 


18. Brown, Smith, and Jones built a steamboat for 
$112 500; of which Brown contributed $43000, Smith 
30000, and Jones the remain@er; they gained $58160 
by carrying freight, and $11840 by carrying passengers ; 
to how much was each entitled ? 
. $26755.552 Brown. 
Ans }s1s006 662 Smith, 
$24577.774 Jones. 
19. A, B, and C enter into partnership; A puts in 
$2000, B $3000 and C 1000 gallons of wine; they gain- 
ed $900, of which C took $800 for his share of the pro- 
fits; to what part of the gain was each of the others en- 
: titled, and what was the price of C’s wine per gallon ? 
$240 A. 
Ans. ; $360 B. 
: $2.50 C’s wine per gall. 


228 COMPOUND PARTNERSHIP. 


COMPOUND PARTNERSHIP. 


Arr, 271. What is Compound Partnership ? 


It is a partnership in which the amount and time of im 
vestment are taken into consideration. 


Art. 272. What is the rule for calculating the gain or 
loss for each person, in compound partnership ? » 


Ruie.—Multipty each person’s capital by the time tt is 
invested ; add the products thus formed, and then find 
what part of the sum the gain or loss is ; multiply the re- 
sulting fraction by the product of each man’s time and 
money ; the products thus found will be each man’s gain 
or loss. 


1, A and B commenced in trade; A put in $350 for 
8 months, and B put in $600 for 7 months; they gained 
$700 ; to what part of the gain is each entitled ? 
aoe $280 for A. 
"($420 for B. 


2. X and Y had been engaged in business and gained 
$8700; X had $3000 in for 3 years, and Y had $4000 
in for 5 years; to how much was each entitled ? 

ae: $2700 for X. 
* ( $6000 for Y. 


3. Wood and Bronson engaged in business; Wood 
' put in $18000 for 17 months, and Bronson put in $24000 
for 6 months; while in business they lost $6500; how 
much of the loss much each bear ? 
wis. | $4420 Wood. 


$2080 Bronson. — 


4. A, B, and C engaged 20 acres of pasture land to 
feed cattle; A had 150 head or the land for 24 days, B 
had 250 head on for 60 days, and C 800 head for 75 days; 


s 


COMPOUND PARTNERSHIP. 229 


they paid $35 for the use of the paswire ground ; how 
much did each have to pay ? $3.06,45 for A. 

Ans. $12.77, for B. 
$19,16—8 for .C, 


137 
5. Three persons who had been in business made up 
their accounts to the ‘1st of January, when the balance 
sheet showed a gain of $18049.60; the first had $22000 
in the business for the year preceding, the second had 
$18600 in for 10 months, and the third had $30000 in 
for 7 months; to what part of the gain was each enti- 
tled ? } $7219.84 for the Ist. 


$5086.70 ,& for the 2d. 
$5743. 05% - for the 3d. 


6. Four persons were engaged in ie Express busi- 
ness ; the first had $4000 employed for 13 months, the 
second $3000 for 18 months, the third $3500 for 20 
months, and the fourth $1800 for 2 years; they lost 

~ $3250; what was the loss of each ? 


% 


$770.98yi, 
$800.6311 
nok $1037.86; ; 


1 
iT: 


acu 
e 7 


ey 


$640.51 442. 


7. On the Ist of January, 1852, James Wilson opened 

a hardware store with a stock of $17200; on the Ist of 
April, Joseph Brooks entered into partnership with him, 
and advanced’ $12000; onthe Ist of July, Abraham 
Miller put in goods to the amount of $16900; on the 
Ist of January, 1853, when the balance sheet was exhib- 
ited, there appeared a net profit of $8060; to how much 
was each partner entitled ? 
: $4053.56424 for Wilson. 

Ans. 4 $2121, 05,85. for Brooks. 
$1885. 38,2 for Miller. 


8. A commenced business with a capital of $10000, on 
the Ist of January, 1852; on the Ist of May, B entered 
into partnership with him, and put in 1500 barrels of 
four; on the first of January, 1853, their profits were 

20 


230 EQUATION OF PAYMENTS. 


$5100, of which B was entitled to $2100; what was the 
value of the flour per barrel ? _ Ans. $7. 


9. A had $3300 at interest for 60 days; B had $4100 
at interest for 45 days, and C had $4950 at interest 
for 70 days; they received $162 interest inoney; what 
did each get, and what was the rate per cent. ? 
$44 for A. 
$41 for B. 
$77 for C. 

8 per cent. 


10. On the Ist of January, 1851, A commenced busi- 
ness with a capital of $23000; two months afterward” 
he drew $1800; on the Ist of April, B entered into 
partnership with him, and put in $18500; on the Ist of 
August, 1851, he drew $10000; on the Ist of January. 
1852, their profits were $8400 ; to how much was each 
entitled 2 " $6577.24 for A. 


Ans. 


$1822.76 for B. 


EQUATION OF PAYMENTS. 


Art. 273. What is Equation of Payments? 


Equation of payments is a rule for finding the time for 
paying the total amount of several sums of money, which 
taken separately, are payable at different times. 


Arr. 274, To find the equated time, 


Ru.z.—WMultiply each sum of money by tts time; add 
the several products thus formed together, and. divide their 
_ sum by the total amount of money; the quotient will be 
the equated time. 


~*~ 
Note.—Equated time and average time are synonymous terms. 


1. A merchant owes $300, payable in 2 months, and 
$900, payable in 4 months ; what is the equated time for 
paying the whole ? Ans, 34 months, 


3 


EQUATION OF PAYMENTS, Os 


2. There are three payments due as follows; $250 in 
2 months, $350 in 4 months, and $500 in 5 months; 
what is the equated or average time for the payment of 
the whole ? Ans. 4 months. 


3. What is the equated time-for paying the sum of 
three notes, of which the first for $100, is due in 5 
months, the second for $150, in 4 months, and the third 
for $150, in 6 months ? Ans. 5 months, 


4, What is the average time for paying the amount 
of four notes, of which the first for $2000, is due in 1 
month, the second, for $8000, in 2 months, the third, for 
$4000, in 8 months, and the fourth, for $1000, in 5 


months ? Ans, 21 months, 


5. A merchant has $1900 to pay in 4 months, $19v0, 
in 6 months, and $1900 in 8 months; what is the average 
time for paying the whole amount? Ans. 6 months. 


6. A person owes three notes; the first is for $300, 
payable in 3 months; the second, for $400, payable in 
6 months; and the third, for $500, payable in 15 
months ; what is the equated time of paying the sum of 
the three notes ? Ans. 9 months. 


7. A person bought a house for $2400, for which he 
agreed to pay as follows: $650 in 8 months, $900 in 8 
months, and the rest in 9 months; what would be the 
mean or equated time to pay the whole ? 

Ans. 7 months, 


8. A person promised to pay $900 in three equal in- 
stalments, viz.: $300 down, $300 in 30 days, and $300 
in 60 days; what is the equated time ? 

Ans, 80 days. 


9. What is the average time to pay, 4 notes, each 
$500, one immediately, another in 20 days, the third in 
60 days, and the fourth in 80 days? Ans. 40 days. 


10. A sum of $2400 is payable in four equal instal- 
ments ; the first in 380 days, the second in 60 days, the 


oa0 EQUATION OF PAYMENTS. 


third in 90 days, and the fourth in 120 days; what is the 
average time to pay the whole? Ans. 75 days. 


11. A person bought a farm for $3000, for which he 
agreed to pay at the following stated times; $500 in 2 
months, $500 in 4 months, $800 in 6 months, $800 in 9 
months, and the remainder in one year; suppose he 
wished to pay the whole at once, what would be the 
average time ? Ans. 6 mo. 18 days. 


12. A grocer bought of a provision merchant, with 
whom he kept an account, 200 barrels of beef, at $15.50 
a barrel; 10 days afterwards, he bought 150 barrels of 
pork, at $13.20 a barrel; 20 days after that he bought 
150 barrels of beef, at $15.80 a barrel; how many days 
after the first purchase would be the equated time to date 
a note ? Ans, 12 days. 


Art. 275. To find the equated time when payments 
are made by date, 


Rurz.— Consider the jirst date as the time from which 
all calculations are to be made ; the sum paid on that date’ 
will of course be multiplied by zero, it being considered as 
paid immediately ; the other payments must be multiplied 
by the number of days between the first date and the date 
oy each payment ; add the several products and divide their 
sum by the sum of the payments ; the quotient will be the 
number of days after the first date that expresses the time 
Jor the payment of the whole,and upon whatever day that 
falls, will be the average or equated time for giving a note or 
calculating interest. If the quotient have a fraction which is 
one half of a day or more, count the fraction as equivalent 
to one day ; if the fraction be less than one half, reject it. 

Lf credit be given, add the time of credit to the date of 
each purchase, and calculate as before from the dates thus 
formed, 


13. A person owes three notes; the first is for $200, 
payable on the Ist of July ; the second for $150, payable 
on the Ist of August, and the third for $250, payable on 


EQUATION OF PAYMENTS. 233 


the 15th of August; what is the average time for the 
whole ? Ars, 28th of July. 


14. There are three notes payable as follows: one for 
$500, on the 12th of February, 1853, the second for 
$400, on the 12th of March, and the third for $300, on 
the 1st of April; what is the average time ? 

Ans. 5th of March, 


15. A merchant has four payments to make ; $260 on 
the 8d February, 1852, $350 on the 10th of March, 
$300 on the Ist of April, and $400 on the 20th of April ; 
what is the equated time ? Ans. 20th of March. 


(16.) 
New York, July 1, 1853. 


James Brower, Bought of G. Tompson, 
April 1. 25 barrels of Pork at $10, $250 
May tle dee ot Beet! $12. $408 

$658 


What is the equated time for giving a note? 
Ans. 20th April. 


(17.) 
A. Cook, ~ Bought of Jones & Co. 


1858. Aug. 1, 450 yds. Muslin at 10c. $45.00 
einai Kamel OD add CIT urea P22 100.00 
“Sept. 5,720 “ Bombazine at 80 576.00 
S Oct. 1,300 “ Cloth at $3.50 1050.00 


What is the equated time for the whole amount ? 
Ans. 18th of Sept. 


(18.) 
- 
BensaMiIn Szaver, Bought of AppreGatse & Co, 


1852. June 18, 1231 yds. Satinet at 78c. 
So mene, 1412 :5% om “932 
66 66 15, 12294 74 66 74 65 
W hat is the average time for payment of the whole ? 
Ans, On the 12th of August. 
20* 


234 EQUATION OF PAYMENTS. 


(19.) 
Cuas. G. Murcu, Bought of Anson Taytor. 


1852. July 5, 500 yds. of Silk Plush at $2.60 
Piao. 1,100, Date sat .68 
ier NOV. 20, 78 pieces binding, at 95 
Sameer, 11 o6)0(7 88 


What is the average time to draw a note for 6 months 
for the whole amount ? Ans. 21st of July 


(20.) 
A purchased of B the following bill of goods, on va- 
rious times of credit : 
May Ist, 1853, A bill amounting to $800 3 months. 


June Ist, “ ys “ 700 3 months. 
patel Ottis st ve i ‘“ 900 4 months. 
- July 25th, “ Z i “1000 6 months. 


When is equated time for payment of the whole ? 
Ans. Oct. 18th. 
(21.) 
A person on various times of credit purchased the fol- 
lowing bills of goods: 


Jan. 17 1849, A bill amounting to $367.20 4 mo. 


pie late We fee “, §901;80. 3 mo: 
Feb. OA, es . re i“ 826.38) 5 mo: 
March 30, ef ae < cc.) 89488. 56 100: 
bE ae) BU . “896.50 4 mo. 


When is the aver age time for payment of the whole ? 
Ans. 6th of July. 


Art. 276. When the amount of mon@ is to be paid 
at a stated time and part is paid before due, to find the 
time for the payment of the remainder, 


Ruite.—Multiply the whole sum by the time when due, 
and from this product subtract the sum of the products of 
the payments made, by their times ; divide the remainder 


EQUATION OF PAYMENTS. 235 


by the balance of money to be paid, and the quotient will 
be the equated time for the payment of the balance. When 
the payments are made by date, count: from the earliest 
date. 


22. A owes B $400, for which B holds A’s note pay- 
able in 5 months; A paid $200 in 4 months; what 
would be the equated time to pay the other $200 ? 

Ans. 6 mo. after date of note. 


23. If a person promises to pay $1000 in 7 months, 
and pays $700 in 4 months, what would be the average 
time to pay the balance ? Ans. 14 months. 


24. A person owes $800, to be paid in 6 months; he 
pays 500 in 4 months; how long would he be entitled 
to keep the balance ? Ans. 9 mo. 10 days. 


25. A merchant owes $2000, which he is to pay in 
one year; he paid $1500 in 8 months; how long may 
he keep the remainder ? Ans. 2 years. 


26. A person owes $500 to be paid on the Ist.of Au- 
gust, 1853; he paid $200 on the Ist of July ; how long 
is he entitled to keep the remainder, $300 2 

Ans. 52 days from Ist of*July, 
Or, on the 22d of August. 


27. A merchant owes $700, which is to be paid on the 
15th of July; he paid one-half of it on the Ist of July ; 
when should he pay the remainder? 

Ans, On the 29th July. 


28. A sum of $1000 is to be paid on the Ist of Janu 
ary, 1854; $400 was paid on the Ist of September, 1853 ; 
$450 was paid on the Ist of December, 1853; when 
should the remainder be paid ? 

Ans. February 20th, 1855. 


29. A man bought a house worth $1500, which was 
to be paid.on the Ist of September, 1854; he paid $400 
on the Ist of November, 1853; $400 on the Ist of Feb- 


236 ' EQUATION OF PAYMENTS. 


ruary, 1854: $400 on the Ist of June, 1854; when 
should the remaining $300 be paid ? 
‘ Ans. 21st November, 1856. 


30. A person borrowed $1800, which he promised to 
pay on the lst of December, 1854; he paid $800 on the 
Ist of July, 1853 ; $600 on the Ist of October, 1853; 
$400 on the Ist of January, 1854; $200 on the Ist of 
August, 1854; when should he pay the remainder ? 

Ans. 11th of February, 1860. 


31. On the 15th of July, 1853, I borrow $700, to be 
paid on the 1st of January, 1854, with interest at the 
rate of 7 per cent. per annum; suppose the rate per 
cent. to be changed to 6 per cent., at what date should I 
pay the money so as to yield the same amount ? 

Ans. 29th January, 1854. 


Art. 277. When purchases and partial payments are 
made at various times, to find the equated time for the 
balance, 


Ruitz.—Average the purchases and payments sepa- 
rately ; if the average date of the payments be earlier than 
that_of the purchases, proceed as in the previous rule ; of 
at be later, multiply the amount of payments made by the 
difference between the two average dates and divide the 
product by the balance to be paid ; the quotient will be the 
number of days previous to the average date of the pur- 
chases, that interest must be calculated on the balance. 

‘ New York, July 1st, 1849. 

Awprew THompson, 
Bought of Enaar Owen. 
Feb. 1, 1849, 1Tonofiron,. . . . § 76.50 
Maye, Eee poise otat 


$226.50 


March 15, 1849, by cash, .. . . , : $200 
What remains due Ist of July, 1849 ? 
Ans. The balance will fall due 147 days after the 15th 


EQUATION OF PAYMENTS. oor 


of March, or upon the 6th of August, which will be 39 
days after the Ist of July; consequently the discount 
for 389 days is to be thrown off the balance, $26.50 ; 
interest 7 per cent. per annum, which gives $26.31 due 
to date. 

Notr.—In these sums the difference in time is calculated by days, and if the 


balance falls due before date, interest must be added to it, if after date, 
discount must be subtracted. 
(33.) 


New York, Jan, 1st, 1853. 
Crark & SmirH, 
Dr. Bought of Samurt Levy. 


May Ist, 1852, To 1000 bu. corn at 40 cts. $ 400 
June 15th, “ “ 2000 “ wheat “90 cts. 1800 
Oct. 15th, “ « 3000 “ corn “40cts. 1200 
$3400 

Cr. 

UUneR Stel Solr Dy Cosh ou ogame |. eum el 
July lst ey es eee rie we om LOU 
Nov. Ist, “ MRR che «<1 GFT ede 2e TO UU 


$2800 
What is the date from which to reckon interest on the 
balance 2 Ans. 26th June, 1853. 


(34.) 
New York, ie Ist, 1854. 
EK. Jonzs, Bought of C, Crarx, 


Jan. Ist, 18538, 200 yd. of cloth at $5, . $1000.00 
Sept ules) 000 yd. of silke oo Sl 300.00 


$1800.00 


March Ist, 1853, by cash, onplomdrete o4 it's! = $500 
August Ist, FC am ome ee 500 
$1000 


From what date must interest be reckoned on the 


238 EQUATION OF PAYMENTS. 


balance, $800, in order to equate the purchases and pay. 
ments ? Ans. 6th June, 1852. 


(35.) 


New York, May 12th, 1854. 
Epear Kurouam, 
Bought of Evrerutr & Co. 


Jan. 3d, 1854, 500 yd. muslin at 40 cts. 
. ithe BOO Bash ges leer 30 
Feb. isthe 400 “ linen “ 1S? 
Cay OC meee 100 “. <cloth, 4 83/500 


Jan.: 20th, by; cash, <5 4) aqgas se oe ees Ue 
Heb; 20th, Sb a8 is AY eae ee 


From what date must interest be reckoned on the 
balance 2 ’ Ans. 


36. A has the following account against B: 
Oct. . Ist, 1851, To merchandise, . § 453.20 


:! 25th, :: : 729.80 
Noy. 12th, 4 % ‘ 431.60 
Dace sto ats ot oe “ 1054.30 

Cr. 
Oct. 20th, 1851, By merchandise, . $ 586.50 
Noy. 19th, “ *¢ cash ; 500.00 


eee Othe ‘¢ merchandise . 1091.81 


What is the balanc€ on the Ist of May 1852, sup. 
posing that 3 mo. credit is given ? Ans. $503.38. 


Notr.—In ths above sum, the amount of each purchase and payment is 
found separately, from the date of purchase or payment to the date of settle- 
ment. ‘I'he difference between the amounts of payments and purchases will 
be the balance due, and this is the only true way to find the interest balance. 


ALLIGATION. ¥ 239 


ALLIG A TION: 
Art. 278. What is Alligation ? 


Alligation is the finding of the value of a compound 
that is composed of ingredients of different values, or it is 
the composition of ingredients in such quantities that the 
compound may have a given value. 


Art. 279. What are the two kinds of alligation ? 


Alligation medial and alligation alternate. 


Arr. 280. What is alligation medial ? 


Lt is the finding of the value of a compound that is com- 
posed of ingredients of different values. 


Art. 281, What is the rule for alligation medial ? 


Ru.e.—Add together the values of the articles mixed, and 
divide the sum by the number of articles in the mixture ; 
the quotient will be the value of a single article of the com- 
pound. 


1. If one pound of coffee at 16 cents, and one pound 
at 18 cents be mixed together, what will the mixture be 
worth a pound ? Ans. 17 cents. 


2. If sugar at 7, 8, and 9 cents a pound be mixed, 
what will be the value of one pound of the mixture 2? 
Ans. 8 cents. 


3. If coffee at 16, 17, 19, and 20 cents a pound be 
mixed, what will be the value of one pound of the mix- 
ture 2 ' Ans. 18 cents. 

4, If tea at 50, 70, 80, and 100 cents a pound be 
mixed, what will be the value of one pound of the 
raixture ? Ans. 75 cents. 


5. A wine dealer mixed several kinds of wine at $1.50, 


240 ALLIGATION, 


$1.75, ana $2 a gallon; what is the average price per 
gallon of the mixture ? Ans. $1.75. 

6. Ifa gallon of alcohol at 50 cts., and a gallon at 
85 cts. be diluted by a gallon of water, what will be the 
price of one gallon of the mixture ? Ans. 45 cents, 

7. During the seven days of a week the thermometer 
stood as follows: 62°, 63°, 619, 642, 633, 68°, and 64° ; 
what is the average height for the week? Ans. 633°. 

8. If gold of 21, 20, 18, and 17 carats fine be melted 
together, how pure ‘will be the compound ? 

Ans. 19 carats fine. 


Note.—The purity, and consequently the value of gold, is reckoned by 


carats; pure gold is said to be 24 carats fine, and is so soft that it easily wears . 


away ; by mixing some other metal with it, it becomes harder; the metal 
with which it is mixed is called alloy, and in reference to gold, like water to 
liquids, is considered of no value; gold of 23 carats fine, expresses 23 parts of 
pure gold and oneof alloy; 22 carats fine expresses 22 parts of pure g gold and 
two parts alloy, &c., the parts of gold and alloy always making 24 


9. A goldsmith melted together 3 oz. of gold 20 carats 
fine, 5 oz. 18 carats fine, and 5 oz. 22 carats fine; what 
is the purity of the mixture ? Ans. 20 carats fine. 


10. A grocer mixed together 60 Ib. of sugar, at 10 
cts. a pound, 75 |b. at 12 cts. a pound, and.75 |b. at 162 
cts. a pound; what was the value of one pound of the 
mixture ? Ans. 15 cts. 


11. A grocer mixed together 35 lb. of coffee at 16 cts. 
a pound, 386 lb. at 15 cts. a pound, and 25 Jb. at 28 cts. 
a pound; what was the value of one pound of the 
mixture ? Ans. 18 cts. 


12. A grocer mixed together 12 lb. of tea at 60 cts. a 
pound, 15 lb. at 72 cts. a pound, and 18 Ib. at 90 cts. a 
pound ; what was the value of one pound of the mixture ? 

Ans. 76 cts. 


18. A liquor dealer mixed together 25 gallons of 
brandy at $1.60 a gallon, 25 gallons at $1.80 a gallon, 
and 18 gallons of water; what was the value of one 
gallon of the mixture, and how much did he make on a 


ALLIGATION ALTERNATE. 241 


gallon, provided the mixture was sold at the average 
price of the liquor ? 
A $1.25 a gallon the mixture. 
ns. te 
45 cts. a gallon gained. 


14, A farmer mixed together 54 bushels of rye at 654 
cents a bushel, 81 bushels at 68% cents a bushel, and 45 
bushels at 814 cents a bushel ; what was the value of one 
bushel of the mixture? Ans. 3.709. 


15. A person bought 32 gallons of wine for 90 cents 
a gallon, 48 gallons at 95 cents a gallon, and 64 gallons 
at $1.08 a gallon; for how much a gallon must he sell 
the mixture to gain 20 per cent. ? Ans $1.196. 


16. A grocer sold 34 lb. of sugar at 5 cent» a pound, 
102 Ib. at 8 cents a pound, 136 Ib. at 10 cents a pound, 
and 34 lb. at 12 cents a pound, and thereby gained 50 
per cent. ? what was the average cost of one pound ? 

: Ans. 6 cents. 


ALLIGATION ALTERNATE. 
Arr. 282. What is Alligation Alternate ? 


It is the composition of ingredients in such quantcties 
that the compound may have a given value. 


Arr. 283. What is the rule for Alligation Alternate ? 


Rute Ist.—ZJf there be two ingredients mixed, of which 
the value of one is as much below the mean value as that 
of the other is above, the number of ingredients will be 
equal, 


2d. Lf there are two ingredients mixed, whose values are 
unequally above and below the mean value, there will be as 
many of the greater value as the mean exceeds the less, and 
as many of the less value as the greater exceeds the mean. 


3d. If there be three or more ingredients mixed, compare 
any two whose values are, the one greater and the other less 
21 


242 ALLIGATION ALTERNATE. 


than the mean ; the result will be the number of ingredi- 
ents for those two ; then compare other two, until the value 


of euch has been used, when the various quantities of each 
value will be found. 


Norre.—When two or more of Jess value than the mean, are compared with 
one greater, there will be as many of the greater value, as the mean exceeds 
each of the less ; proceed in like manner when several of a greater value are 
com pared with one of. less. 

There will be a variety of answers, since any two, (the one greater, the other 
less,) may be compared ; and likewise when equal parts or multiples of the 
answers by the previous rules are mixed, they vive the same mean value of 
the mixture. The form generally used is the “following, where each differ- 
ence is placed opposite to the value to which it belongs. 


- 


ft Drains 15 6+3-+1 = 10, 
10{ 9 Q ato: 18 19 3 
12 J+1 = 4 at 12. Olt? co 
24 3 &c. 


17. A grocer wishes to mix sugar at 8 and 10 cents a 
pound, so that the mixture may be worth 9 cents a 
pound; in what quantities shall he mix it? 

Ans. Equal quantities, as 1 lb, of each, 5 lb. of 
each, &c. 


18. A grocer wishes to mix tea at 95 cents a pound 
with tea at 63 cents a pound, so that the mixture may 
be worth 79 cents a pound ; how shall he mix it 2 

Ans. Equai quantities of each. 


19. A grocer mixed coffee worth 19 cents a pound 
with coffee worth 13 cents a pound, in such quantities as 
to have a mixture worth 15 cents a pound ; in what pro- 
portion did he mix the different qualities ?. 

oe § 4 1b. at 18 cents. 
"(2 lb. at 19 cents. 
Novre.—If these quantities be divided or multiplied by the same number 
the results when mixed will give the same average value. 

20. How can wine worth 85 cents a gallon be mixed 
with wine worth $1.20 cents a gallon, so as to form a 
mixture worth $1 a gallon ? 

Ans, $29 gallons at 85 cents. or in pro- 
115“ at $1.20 cts. § portion. 


21. In what proportion can alcohol worth 65 cents a 


ALLIGATION ALTERNATE. 943 


gallon be dil..ed with water, so as to form a mixture 
worth 60 cents a gallon ? 
At te 60 gallons of alcohol. 
is, m 
of water. 
22. In what proportion should gold of 18, 20 and 23 
carats fine be melted together so as to form a compound 
of 19 carats fine ? 
Ans. 5 of 18, 1 of 20, and 1 of 28. 


23. In what proportion should gold of 17, 18 and 22 
carats fine be melted together to form a compound of 20 
carats fine ? 

Ans. 2 of 17, 2 of eighteen, and 5 of 22. 


24. In what quantities should sugar at 8, 10, 12 and 
15 cents a pound be mixed together to form a mixture 
worth 11 cents a pound? 

Ans. 1 Ib. at'8 cts., 4 lb. at 10 cts., 3 1b. at 12 cts., 

and 1 lb. at 15 cents. 
Or—4 Ib. at 8 cts., 1 lb. at 10 cts., 1 lb. at 12 cts. 
and 3 Ib. at 15 cents. 


25. How can wine worth $1.75, $1.874, be mixed to- 
gether and diluted with water, to form a mixture worth 


$1.624 a gallon ? ‘ ae gallons at $1.75. 
Ans, 71624" 9 “at 1.874. 
37%  “ — of water. 


26. In what proportions can gold of 16, 18 and 21 
carats fine be further alloyed so as to form a mixture of 
19 carats fine ? 


2 of 16 carats fine. 2 parts of alloy. 
i Pe komd Lan 2p cnt ee ones. fine, 
DN Alte T ‘c eer 9 6 IQ wwe 
No alloy. Pag. hg ald Sil 


27. In what proportion can tea at 564, 60, 68, and 
75 cents a pound be mixed so as to form a compound 


worth 65 cents a pound ? 10 at 564 cents. 
: . oe 8 66 60 66 
2 5 66 68 (74 


88“ 75 « &, 


244 ALLIGATION ALTERNATE. 


28. How many pounds of tea at 60 cents a pound 
must be mixed with 25 lb. of tea at '75 cents a pound, so 
as to form a mixture worth 70 cents a pound ? 

Ans. 124 lb. at 60 cents. 


29. How many pounds of sugar at 9 cents a pound 
must be mixed wih 50 Ib. at 8 cents a pound, so as to 
form a mixture worth 8} cents a pound ? 


Ans. 50 Ib. 


30. How many pounds of sugar at '7 and 11 cents a 
pound must be mixed with '75 lb. at 12 cents a pound, 
so as to form a mixture worth 10 cents a pound ? 

Ans. 75 Ib. of each. 


31. How many ounces of gold of 15, 18 and 20 carats 
fine must be mixed with 7 ounces of 19 carats fine, so 
that the compound may be 17 carats fine ? 

Ans. 21 oz. of 15 carats, 7 of 18 and 7 of 20. 


32. How many gallons of oil at 7s., ‘7s. 6d., and 9s. 
a gallon must be mixed with 24 gallons of oil at 9s. 6d. 
a gallon, so as to form a mixture worth 8s. a gallon ? 
Ans. 86 gall. at 7s., 24 at 7s. 6d., and 12 at 9s. 
Or, 48 gall. at 7s. 712 at ‘Ts. 6d., and 48 at 9s., &e. 


33. A liquor dealer has a barrel containing 32 gallons 
which he wishes to fill with water aud brandy at $2.24 
a gallon, so that the mixture may be worth $2.10 a gal- 
lon; in what proportion are they to be mixed? 

; 30 gallons of brandy. 

Ans. "* 
2 of water. 


34. How can a hogshead containing 63 gallous be 
filled with wine at $1.20 and $1.08 a gallon, so tht the 
mixture may be worth $1.17 a gallon? 

Ans, 471 gall. at $1.20 and 152 at $1 08. 


INVOLUTION. 245 


ENG O Eel Ne 


Arr. 284. What is Involution 2 


Involution is the multiplication of any number by itself 


a certain number of times. 


Arr. 285, If a number be multiplied by itself, what 


is the product called ? 


The square of that number. 


Art. 286. If a number be involved three times, that 
is, once as a multiplicand and twice as a multiplier, what 


will the product be called 


The cube, or third power of that number. 


Art. 287. If a number be involved four, five, or six 


times, what will the product be called ? 
The fourth, fifth, or sixth power of that number. 


O DWr~T DOP ow WD 


. What is the square of 9 2 Ans. 81. 
. What is the square of 14? Ans. 196. 
. What is the square of 23 ? Ans. 529. 
. What is the square of 54? Ans. 2916. 
. What is the square of 841 ? Ans. 707281. 

What is the square of 3759? Ans. 14130081. 
. What is the square of 75.4? Ans. 5685.16. 
. What is the square of 9.145? Ans, 83.631025. 
. What is the square of 316.05 ? 


Ans. 99887.6025. 


. What is the square of .75. Ans. .5625. 
tie 
12. 


What is the square of .125? Ans. .015625., 


What is the square of .04375 ? 
Ans. .0019140625. 
DA hg 


20. What is the square of 1194? Ans, 14852,4. 
21. What is the cube of 7 ? Ans. 343. 
22. What is the cube of 9 ? Ans, 729. 
3. What is the cube of 17 2 ~ Ans. 4913. 
24. What is the cube of 251 Ans. 15625. 
25. What is the cube of 79 ? Ans. 493039. 
26. What is the cube of 175 ? Ans. 5359375: 
27. What is the 4th power of 8? Ans. 4096, 
28. What is the 5th power of 16% Ans. 1048576. 
29. What is the cube of 3.5 2? Ans. 42.875. 
30. What is the cube of .27 ? Ans. .019683. 
31. What is the 4th power of 2.05 ? 
Ans. 17.66100625. 
32. What is the cube of 5% ? Ans. 2/55. 
33. What is the cube of 71 ? Ans. 4214, 
34, What is the cube of 132? Ans. 259932. 
35. What is the 4th power of 58? Ans. 8341737, 


INVOLUTION. 
. What is the square of 2? Ans, #5. 
. What is the square of 7? Ans. ¢%. 
. What is the square of % ? Ans. y- 
. What is the square of 13? Ans. 225. 
. What is the square of $$ Ans, 3238, 
. What is the square of 82? Ans. 76;%. 


. What is the square of 12,4? Ans. 161545. 


. What is the 5th power of 332 Ans. 741758). 


EVO. UTION. 247 


EVOLUTION. 
Arr. 288. What is Evolution 2? 


Hvolution is the process of separating a number into 
equal factors. 


Art. 289, What is a square root ? 


Sguare root is the separating of a number ento equal 
two factors, 


Arr. 290. To extract the square root of a number, 


Ruize.—I. Commence at the units, place and separate 
the gwen number into periods of two figures each ; 

I. ind the greatest square number in the left-hand 
period, and place its root to the right of the given number, 
as in long division, and call et the first figure of the root; 
square this figure and subtract the square from the left 
pervod, and to the remainder annex the next period consist- 
ing of two figures, to form the next dividend ; 

III. Double the root already found for @ triad divisor, 
and find how many times it rs contaened in all the figures 
of the dividend, except the last ; place the quotient to the 
right of the first figure of the root, and also to the right of 
the triad divisor to form tke complete divisor ; 

IV. Multiply the divisor thus formed by the second 
Jigure of the root ; subtract the product from the divadend, 
annex the next period to the remainder, and proceed from 
the section 3d for other jigures of the root. 


Nors.—No figure of the root can exceed 9. The remainder ‘s sometimes 
equal to, and often greater than, the diviser for the time being. 


Arr. 291, To extract the square reot of a decimal 
fraction, 


Find the square root of tie first two decimals to the 
right of the point, and then proceed as in whole numbers. 


Arr. 292, To extract a square root of a vulgar fraction, 


Find the square root of the numerator, and then the 


248. EVOLUTION, 


square root of the denominator, or reduce it to a derimal 
- fraction, and extract the root. 


1, What is the square root of 162 Ans. 4. 
2. What is the square root of 81? Ans. 9. 
3. What is the square root of  ? Ans, 3. 
4, What is the square root of ;84,? Ans. 5. 
5. What is the square root of .09 2 Ans. .3. 
6. What is the square root of .49 ? Ans. .7. 
7. What is the square root of 1600 ? Ans. 40. 
8. What is the square root of 1764 ? Ans, 42. 
9. What is the square root of 2809 ? Ans. 538. 


— 
joo) 


. What is the square root of 6241 ? Ans. 79. 
. What is the square root of 27889 ?. Ans. 167. 


. What is the square root of 251001 2 
Ans. 501. 


. What is the square root of 6275025 ? 
Ans. 2505. 


. What is the square root of 38950081 ? 
Ans. 6241. 


. What is the square root of 5647.5225 ? 
Ans, 75.15. 


16. What is the square root of 656748.16 ? 
Ans. 810.4. 


17. What is the square root of 83687.525625 2? 
Ans. 60.725. 


18. What is the square root of 160048.0036 2 
Ans. 400.06 


19. What is the square root of .205209 ? 


p—— eed 
wo 


pom 
ise) 


—" 
Te 


fond 
a 


Ans, .458, 


20. What is the square root of .022201 2 
Ans. .149, 


EVOLUTION. 249 


21. What is the square root of 185% Ans, 11.614. 


22. What is the square root of 7994? 
Ans. 89.409. ~ 


23. What is the square root of 19000 ? 
Ans, 137.844. 


What is the square root of .9 ? Ans, .9486. 
25. What is the square root of .5 ? Ans, .7071. 
26. What is the square root of .1 ? Ans, .3114. 
27. What is the square root of .7842 Ans. .8854. 
28. What is the square root of 1.5? Ans. 1.2247. 
29. What is the square root of 196.425 2 
Ans. 14.0151. 
30. What is the square root of .00794 2? 
Ans, .0891. 
31. What is the square root of .000625. 
Ans. .025. 
82. What is the square root of 86432.9864 2? 
Ans. 293.99. 


wv 
> 


Arr. 293. What is a mean proportional between 
two numbers ? 


It is the square root of ther product. 


33. What is the mean proportional between 9 and 16 ? 


Ans. 12, 
34, What is the mean proportional between 18 and 
32 2 Ans. 24, 


5. What is the mean proportional between 500 and 
Ans, 547.722. 


6. What is the mean proportional between 182? and 
Ans. 20.5389, 


(ae) 

: SS 
ve OF © & 

‘~~ i] 


80.061 ? Ans. 7'7.736. 


250 EVOLUTION, 


38. What is the mean proportional between .01875 
and .006 2 ) Ans. .0106. 


Arr. 294. To extract the cube root of a number, 


Rutzt.—lst. Separate the given number into periods 
of three figures each, commencing at the units place ; 


2d. Hind the greatest cube in the left hand period, ard 
place its cube root to the right of the given number as in 
long division, and call it the first figure of the root. 

Subtract the cube of this number from the left hand pe- 
riod, and to the remainder annex the next period, which 
number thus formed consider as a new dividend. 


3d. Hor a partial divisor, square the root already found, 
multiply the square by 800 and divide the product into the 
dividend to find the next figure of the root. 


4th. Multiply the figure last placed in the rovt by that 
previously there, and multiply their product by 80. 

Square the figure last placed in the root, and add the 
square to the products formed by multiplying by 300 
and by 30; the sum thus formed will be the complete di- 
vesor. 

5th. Multiply the complete divisor by the figure last 
placed in the root, subtract the product from the dividend, 
and to the remainder annex the next period for a new divi- 
dend ; for another figure in the root commence at section 
3, and proceed as before. 


Arr. 295. To extract the cube root of a decimal frac- 
tion, 


Extract the cube root of the first three figures for the 
Jirst figure of the root, bring down the other decimals an 
periods of three figures each, (annexing ciphers uf neces- 
sary,) and proceed acerrding to the rule. 


Arr. 296. To extract the cube root of a vulgar frac 
tion, 


EVOLUTION, 951 


Extract the cube root of the numerator cmd denomina- 
tor separately ; or reduce to a decimal fraction and -ex- 
tract the cube root, 


Notre.—When the root has been extracted to four or five figures, there will 
be but a small error in continuing to divide by the last divisor, for other fig- 
ures of the root. 


39. What is the cube root of 216 2 Ans. 6 
40. What is the cube root of 343 2 Ans. 7 
41. What is the cube root of 729 ? Ans. 9. 
_ 42. What is the cube root of 22? Ans. 3. 
43. What is the cube root of 34% ? Ans. 385. 
44, What is the cube root of 1728 2 Ans. 12 
45. What is the cube root of 8000 ? Ans, 20 


46. What is the cube root of 1250002 Ans. 50. 
47. What is the cube root of 4096 2 Ans. 16. 
48. What is the cube root of 9261 2 Ans, 21. 
49, What is the cube root of 46656 2 Ans. 36. 


50, What is the cube root of 1815848 2 
Ans. 122. 


51. What is the cube root of 16777216 2 
Ans. 256. 


52. What is the cube root of 28652616 2 
Ans. 306. 


53. What is the cube root of 651714363 2 
Ans. 867. 


54. What is the cube root of 32891033.664 2 
Ans. 820.4. 


55. Extract the cube root of .064. Ans. 4. 
56. Extract the cube root of .000729. Ans. .09. 
57. Find the cube root of .000003375. Ans. .015. 
58. What is the cube root of .01252 Ans. .282. 
59. What is the cube root of .0066592 2? Ans. .1884. 


B52 MENSURATION. 


MENSURATION. 


Art, 297. What is Mensuration 2 


Mensuration is the method of estimating, from certain 
given parts, the length of lines and the contents of ne 
and solids. 


Arr. 298. What is a triangle ? 


It is a plane figure bounded by three 
straight lines. 


Art. 299. What is a right-angled tri- 
angle ? 


It is triangle that contains a right an- 
gle. 


Art. 300. What is the longest side of a right-angled 
triangle called ? 


It is called the hypothneuse. 


Art. 301. To find the hypothenuse of a right-angled 
triangle, when the other two sides are known, 


Ru.te.—Add the squares of the other two sides; the 
square root of the sum will be the hypothenuse. 
Art. 230. To find a side of a right-angled triangle, 


when the hypothenuse and the other side are known, 


Rutu.—Srom the square of the hypothenuse, subtract 


MENSURATION, 253 


ere square of the given side; the square root cf the re- 
mainder will be the length of the side required. 


1. The two sides of a right-angled triangle are 40 anA 
30 feet ; what is the length of the hy pothenuse ? 
Ans. 50 feet. 


2, The two sides of a right-angled triangle are 7 yards 
and 24 yards; what is the length of the hypothenuse ? 
Ans. 25 yards. 


2. The two sides of a right-angled triangle are 304 feet 
and 104 feet; what is the length of the hypothenuse ? 
Ans. 1083 feet. 


4, The two sides of a right-angled triangle are 134 and 
162 feet; what is the length of the hypothenuse ? 
Ans. 21.61-- feet. 


5. The two sides of a right-angled triangle are 14.34 
rods and 29.05 rods; what is the length of the hypo- 
thenuse ? Ans. 32.3 rods. 


6. The hypothenuse of a right-angled triangle is 411 
feet and_the base is 205 feet ; what is the length of the 
other side or perpendicular ? Ans, 356.224 feet. 


7. The hypothenuse of a right-angled triangle is 64 
rods and the perpendicular is 34.75 rods; what is the 
length of the other side or base? Ans. 53.744 rods, 


8. The hypothenuse of right-angled triangle is 432 
yards and one side is 18? yards; what is the length of 
the other side ? Ans. 89.528 yards. 


9. A ladder is placed with one end on the side walk 
10 feet from a house, and just reaches the gutter which 
is 30 feet. high; how long is the ladder ? 

Ans. 31.62 feet. 


10. A person is standing 350 feet from the bottom of 
a tower which is 2624 feet high; how many feet is it 
from him to the top of the tower ? Ans. 4374 feet. 
ae 


254 MENSURATION, 


11. A room is 45 feet square ; how far is it from one 
corner to the opposite ? Ans. 68.64 feet. 


12. The height of the foremast of a vessel is 90 feet, 
and the distance from the foot of the mast to the extrem- 
ity of the bowsprit is 45 feet; about how long is the 
rope that reaches from the top of the mast to the end of 
the bowsprit ? Ans. 100.62 feet. 


13. The two masts of a schooner were placed perpen- 
dicular to the deck and 25 feet apart; one mast was 90 
feet high and the other 100 feet high; how long was the 
rope that reached from the top of one mast to the top of 
the other ? Ans, 27 feet (nearly.) 


14, A ladder 50 long placed in the street just reaches 
to the tops of two houses on opposite sides; one of the 
houses is 35 feet high and the other 80 feet ; what is the 
width of the street ? Ans. 75.7 feet. 


15. If the two sides of any triangle are 75 feet and 
90 feet, and the perpendicular to the third side 45 feet, 
what is the length of the third side ? 

: Ans. 137.94 feet. 


Arr. 303. To find the area of a triangle, 


Ruitz.—Multiply the base by half of the altitude ; 
the product will be the area of the triangle. ~ 
Notr.—The surface of similar figures are proportional to the squares of their 
corresponding sides. 
16.-What is the area of a triangle whose base is 13 
feet, and whose altitude is 22 feet ? 
58 oe 
Ans. 153 square yards. 
17. What is the area of a triangle whose base is 500 
yards, and whose altitude is 270 yards ? 
Ans. 67500 sq. yd. 
18. What is the area of a triangle whose base is 75 
chains, and whose altitude 30 chains ? 


Ans. 112 A. 2 R, 


MENSURATION. 255 


19. What is the area of a triangle whose base is 
829.05 yards, and altitude 516 yards ? 
Ans. 130939.9 sq. yd. 
20. What is the area of a triangle whose base 17.3% 
feet, and whose altitude 11.25 feet ? 
Ans. 97.59375 sq. ft. 


Axt. 304, What is parallelogram ? 
It is a figure of four sides having the / , 
opposite sides equal and parallel, 


Art. 305. What is a rectangle ? 


It is a parallelogram that has all its 
angles right. 


Art. 306. What is a square ? 


Jt ts a parallelogram that has its 
angles right and all of tts sides equal. 


Art. 307. To find the area of a parallelogram, 


Multiply the base by the altitude, and the product will be 
the area. 


21. What is the area of a rectangle whose base is 24 
yards, and altitude 15 yards ? Ans. 360 sq. yd. 
22. What is the area of a rectangle whose base is 425 
feet, and altitude 300 feet ? 
Ans. 2 A. 3 RB. 28 sq. p. 9 sq. yd. 6 sq. ft. 
23. What is the area of a parallelogram whose base is 
'1134-miles, and whose altitude is 42 miles ? 
Ans. 542 sq. m. 
24, What is the area of a parallelogram whose base is 
95 feet, and whose altitude is 33.534 feet ? 
Ans. 31662 sq. ft. 


256 . MENSURATION. 


25. What is the area ofa parallelogram whose base 1s 
843 chains, and the altitude 174 chains ? 
Ans. 150 A. 3 R. 16 sq. p. 


26. What is the area of a rectangle whose base is 
40.775 inches, and altitude 14.034 inches ? 


Ans. 
27. What is the area of a square whose side is 444 
yards ? Ans. 1980.25, 
28. What is the area of a square whose side is 77.08 
inches ? Ans. 5941.8264. 


29. If the area of a rectangle is 553.25 square feet, and 
one of the sides 292 feet, what is the length of the other 
side ? Ans, 18.59 sq. ft. 


30. There is a rectangular piece of land containing 
14A.3 RK. 20 sq. p.; it is 450 feet wide; what is the 
length of it ? Ans. 1439.9 ft. 


31. A room 25 feet by 40, is to be covered by carpet, 
3 of a yard wide; how many yards will it take ? 
Ans. 1484, yd. 


32. The front of a house 224 feet wide ca ‘32 feet 
high, is to be painted at the rate of 25 cents per square 
yard; it contains 5 windows, each 5 feet by 3, and one 
door 6 feet by 4; what will be the cost of painting the 
house ? Ans. $17.25. 


33. How many marble slabs, 15 in. square, will it 
take to pave a floor 32 feet long and 25 feet wide? 
What will be the cost at $8 a square yard for the 
marble, and 40 cents a square yard for Jabor ? 

‘Bn: 512 slabs. 
$193.42. 

34, What is the ene of the side of a square whose 
surface is equal to that of a rectangle having its sides 12 
and 48 feet long ? Ans. 2+ feet. 


35. Ifa rectangle have one side 18 yards long and the 
other 40 yards long, what will be the side of the square 
that contains the same number of square er ds t 

Ans. 26.883 Syd. 


MENSURATION. PAs ys 


36.- How many times larger is a square whose side is 
16 feet, than one whose side is 4 feet? Ans. 16 times. 
37. How many times larger is a square whose side is 
20 feet, than one whose side is 12 feet ? 
Ans. 2% times, 
38, If one square whose side is 74 feet be placed 
inside of another whose side is 20 feet, how many square 


feet will there be between the two squares ? 
Ans. 345.75 sq. ft. 


Art. 308. What is a trape- 
zoid ? 

Jt ws a four sided figure, 
two of whose sides only ure 
parallel, 


Art. 309. To find the area of a trapezoid, 


Rurze.—Multiply the sum of the lengths of the parallel 
sides by half the perpendicular distance between the same 
sides. 


39. What is the area of a trapezoid whose parallel 
sides are 25 and 40 feet, and the distance between them 
or altitude is 173 feet ? Ans. 5762 sq. ft. 


40. What is the area of a trapezoid whose parallel 
sides are 163 and 14, feet, and the altitude 429 feet ? 
> Ans, 7422 sq. ft. 


41. What is the area of a trapezoid whose parallel 
sides are 17.45 and 36,075 ft., and the altitude 200 
feet ? Ans, 5852.5 sq. ft. 


Art. 310. What is a circle? 


It is a plane figure enclosed by a 
curve line, of which every point is 
equally distant from a point within tt, Wy 


called the centre. 
22* 


258 MENSURATION, 


Art. 311. What is the circumference ? 


It is the curve line that bounds the circle. 
Art. 312. What is the diameter of a circle 2 


It is the straight line that passes through the centre and 
as terminated each way by the circumference. 


Art. 313. What is the radius of a circle ? 


It is the straight line that passes from the centre to the 
circumference. 


Art. 314. To find the circumference of a circle when 
the diameter is known, 


Rutz.— Multiply the diameter by 3.1416, and the pro- 
duct will be the circumference. ei 


Art. 315. To find the diameter when the circumfer- 
ence is known, 


Rute.—Divide the circumference by 3.1416 and the 
quoteent will be the diameter. 


NoTeE.—It is generally said that the circumference of a circle is little more 
than 3 times the diameter ; 37 is near enough for ordinary purposes; 3.1416 
is nearer still, and is sufficiently exact except in cases where extreme accu- 
racy is required. 


42. What is the cireumference of a circle whose diam- 


eter is 800 feet 2 Ans. 942.48. 
43. What is the circumference of a circle whose di- 
ameter is 932 yards ? Ans, 293.525 yards. 
44, What is the circumference of a circle whose di- 
ameter is 18.625 chains 2 Ans. 234.0492 rods. 
45. What is the diameter of a circle whose circumfer- 
euice is 450 rods 2 Ans, 148.24 rods. 


46. What is the diameter of a circle whose circumfer- 
ence is 3754 feet ? Ans. 119.62 feet. 


MENSURATION. 259 


47. What is the diameter of a circle whose circumfer- 
ence is 645.375 chains ? Ans. 205.48 chains. 


48, What is the circumference of a circle whose diam- 
eter is 1649 feet 2 Ans. 5180.4984 feet. 


49. If the distance of the earth from the sun is 
95000000 miles, what is the circumference of its orbit ? 
Ans. 596904000 miles. 


50. The diameter of the earth is 7912 miles; what is 
the distance round it ? Ans, 24856.5392 miles. 


51. How many times will a thread that is 100 yards 
long, go round a circle 19 inches in diameter ? 
Ans. 60.311 times. 
52. The wheel of a carriage is 44 feet in diameter ; 
how many times will it turn in gomg a mile? 
Ans. 373.48 times. 


Art. 316. To find the area of acircle when the diam- 
eter is known, 


Rurzu.—Multiply the square of the radius by 3.1416, 
and the product will be the area. Or, 


Find the circumference and multiply it by one half the 
radius ; the product will be the area. 


Art. 317. To find the area of a circle when the cir- 
cumference is known, 


Ruie.—Find the diameter and multiply the circumfer- 
ence by one half the radius. 


Art. 318. To find the diameter of a circle when the 
area is known, 


Rue.—Divide the area by 3.1416 ; the square root of 
the quotient will be the radius. 


53. What is area of a circle whose diameter is 12 
feet ? Ans. 113.0976 sq. feet. 


260 MENSURATION. 


54. What is the area of a circle whose diameter is 720 
yards ? Ans. 407151.36 sq. yards. 


55. What is the area of a circle whose radius is 274 . 
rods ? Ans. 2375,.885 sq. rods. 


56. What is the area of a circle whose radius is 55.'75 
ehains ? Ans. 156228.6264 sq. rods. 


57. What is the area of a circle whose circumference 
is 450 feet ? Ans. 16114.4 sq. feet. 


58. What is the area of a circle whose circumference 
is 1784 yards ? Ans, 2544.014 sq. yds. 


59. What is the area of a circle whose circumference 
is 1498.476 chains ? Ans, 


60. A person had a piece of land in the form of a cir- 
cle that measured 43 rods and 38 yards through the cen- 
tre; how many acres did it contain ? 

Ans. 9 A. 1 R. 9.28+ sq. p. 


61. What is the diameter of a circle whose area is 
250 square yards 3 Ans. 17.84 yd. diameter. 


62. A piece of land is in the form of a circle and con- 
tains 15 acres; how many rods are there in the circum- 
ference ? Ans. 173.63+ rods. 


63. A semi-circular piece of land contains 1 square 
mile; how many yards are there in the diameter ? 
Ans. 2808.55-+ yards. 


64. Which covers the greater surface, a circle 3 feet 
in diameter, or a square whose side is 3 feet ? 
Ans. 1.9814 sq. ft. more in the square. 


65. Which contains the greater surface, a circle 25 
yards in circumference, or a square whose 4 sides meas- 
ure 25 yards? Ans. 10.6785 sq. yd. more in the circle. 


66. Ifa circle 23.5 feet in diameter be placed: inside 
of another 50.25 feet in diameter, how many square feet 
will there be between the two circles ? 

As. 1549,446 sq, feet. 


MENSURATION. 261 


67. What would be the side of a square having the 
same amount of surface as a circle 40 feet in diameter 2? 
Ans. 35.449-+ feet. 


68. What is the diameter of a circle that contains the 
same amount of surface as a square whose side is 28 
feet ? Ans, 28.209 feet. 


69. How many times larger is a circle 50 feet in di. 
ameter, than one 20 feet in diameter ? 
Ans. 64 times. 


Art. 319. What is a prism ? 


. It is a solid figure whose faces are 
parallelograms, and its bases, parallel 
planes, having three or more sides, 


Art. 320. What is a parallelo- ET RAY, 
pipedon ? 


It is a prism whose bases are 
parallelograms. 


Art, 321. When is a parallelopi- 
pedon rectangular ? 


It is when the faces are rectangles, 
and consequently, perpendicular to 
the bases. 


| 
| 
L. 


262 MENSURATION. 


ART. 322. What is a cube 2? 


It is solid that has all its faces 
end bases equal squares. 


- Art. 323. To find the solidity of a prism, 
Ruiz.—Multiply the area of its base by its altitude. 


70. What is the solidity of a prism whose base is 25 
square feet, and the altitude 124 feet ? 
Ans. 3124 cubic feet. 


71. What is the solidity of a prism whose base is 4 
feet square, and the altitude 15 inches ? 
Ans. 20 cu. ft. 


72. What is the solidity of a rectangular parallelopi- 
pedon whose base is a square of which the side is 12 
inches, and the altitude 15 inches? Ans, 14 cu, ft. 


73. What is the solidity of a rectangular parallelopi- 
pedon whose base is a rectangle of which the length is 4 
feet, the breadth 3.5 feet, and the altitude 234 inches ? 

Ans. 274 cu. ft. 


74. How many bushels will a rectangular box hold, 
which is 20 inches long, 15 inches wide, and 114 inches 
deep ? Ans. 1.604 bu. 


75. A beer vat is 7 feet long, 5 feet wide, and 8 feet 
deep ; how many hogsheads will it hold counting 282 
cubic inches to the gallon? Ans, 27 hhd. 14 gal. 3 qt. 


76. A bin was made 3 ft. 5 in. wide, 2 ft. 6 in, Jong, 
and six ft. high ; how many bushels will it hold ? 
Ans. 41 bu. 0 pk. 6 qt. 


77. A man has 4000 bushels of grain; he has ground 
room 15 feet by 12 ft. 6 in.; how high must he make a 
bin to contain the grain ? Ans. 26 ft. 64 in, 


MENSURATION,. 263 


78. A cistern is 5 feet deep and 6 feet square at che 
bottom ; how many gallons of water does it hold, at 231 
cubic inches to the gallon ? Ans. 18462% gal. 


79. A cistern is 14 feet deep and 5.5 feet square; if 
3 galicns run into it in a minute, how long will it take 
to fill it 2 Ans. 17 hr. 36 min. 


80. A piece of timber is 22 in. by 154 on each end, 
and is 56 feet long; how many tons does it contain ? 
Ans. 1 cd. 4.6 cu. ft. 


81. A pile of wood is 110 feet iong, 8 feet high, and 
4 feet deep; how many loads are there in the pile, 
counting 2 loads to a cord ? Ans. 55 loads. 


82. How many bricks, each measuring 80 cubic inches 
will it take to build a wall 30 feet long, 10 inches thick 
and 8 feet high ? Ans, 4820 bricks. 


83. A box is 4.25 feet long, 3 feet wide, and 3.75 feet 
high ; what are the solid contents, and how many square 
feet of surface does it contain, not counting the top ? 
Ans, 


84. If a room be 40 feet long, 25 feet wide, and 15 
feet high, how long will be the distance from the rear 
right hand corner at the floor to the front left hand 
corner at the ceiling ? Ans. 49.5 feet (nearly.) 

85. What is the side of a cube that is equal in solidity 
to a rectangular parailelopipedon whose sides are respec- 
tively 6, 12, and 24 feet ? Ans. 12 feet. 

86. What is the side of a cube whose solidity is the 
same as that of a rectangular parallelopipedon whose 
sides are 80, 75, and 60 feet ? Ans. 71.18 cu. ft: 

87. If the materials that compose the Chinese wall, 
which is 1500 miles long 30 feet high, and 20 feet thick, 
had been put together mm form of a cube, how high 
would it have been ? Ans. 1681.2 ft. 

88. How many times larger is a cube whose side is 
64 feet, than one whose side is 32 feet ? 

Ans. 8 times, 


264 MENSURATION. 


Art. 324. What is a pyramid ? 


It is a solid having three or more 
sides at the base, and gradually 
tapering to a point. 


Art. 325. To find the solidity 
of a pyramid, 


Ruiz.—Multiply the area of the 
base by one third of the altitude. 


89. What is the solidity of a pyramid whose base is 
5 feet square, and whose altitude is 14 feet ? 
Ans. 116% cu. & 
90. What is the solidity of a pyramid whose altitade 
is 9 feet and the base a rectangle 54 ft. by 3+ ft. ? 
Ans. 55 cu. fi. 


91. How many cubic ft. in astick of timber 30 feet long, 
5 ft. 3 in. square at one end, and gradually tapering to a 
point at the other end ? Ans. 275% cu. ft. 


Art. 326. What is the frustrum of 
a pyramid ? 


It is that part which is left, after a 
smaller pyramid is cut of by a plane 
parallel to the base. 


Art. 327. To find the solidity of the frustrura of a 
pyramid, 


Rutzu.—Add together the upper base, the lower base and 
the mean proportional between the two bases ; multvply the 
sum thus found by one-third of the altitude of the frus 
trum, and the product will be the solidity. 


MENSURATION. .. 265 


92. If the upper base of a frustrum of a pyramid be 
40 square yards, and the lower base 90 square yards, 
while the altitude is 30 yards, what will be the solidity ? 

Ans, 1900 cu. yards. 


93. What is the solidity of the frustrum of a pyramid 
whose upper base is 30 square feet, the lower base 534 
square feet, and the altitude 27-feet ? 

Ans. 1110 cu. feet. 


94. How many solid feet ina stick of wood in the 
form of the frustrum of a pyramid, one end measuring 
36 square feet, the other 25 square feet, and the length 
125 feet ? Ans. 387912 solid feet. 


95. Ifa stick of timber in the shape of the frustrum of 
a pyramid, measure 34 feet square at one end, 24 feet 
square at the other and 140 feet long, what will be the 
solidity ? | Ans. 12712 cu. feet. 


Art. 328. What is a cylinder 3 


It is a solid whose bases are circles, 
and every section parallel to its bases, 
is likewise a circle, 


Arr. 329. To find the solidity of a cylinder, 


Rutze.—Multiply the area of the base by the altitude ; 
the product will be the solidity. 


96. A cylinder is 4 feet in diameter and 15 feet high, 
how many cubic feet does it contain ? 
Ans. 188.496 cu. feet. 


97. What is the solidity of a cylinder 14 feet in diam 
eter and 27 feet long ? Ans, 4156.3368 cu. feet. 
23 


266 MENSURATION. 


98. What will it cost to have a cistern dug, 7 feet in 
diameter and 12 feet deep, at 452 cents per cubic yard ? 
Ans. $22.45, 


99. What is the difference between a cistern 5 feet 
deep and 8 feet 5 inches square, and one of the same 
depth and 3 feet 5 inches in diameter ? 

Ans. 12.526 cu. feet. 


100. What is the diameter of a cistern that is 10 feet 
deep and contains 400 gallons of water ? 
Ans. 2 ft. 6.11 in. 
101. A cylindrical vessel is 4 feet 6 inches in diame- 


ter and 5 feet 4 inches deep; how many bushels will it 
contain ? Ans. 68 bu. 0 pk. 5 qt. 


102. How many cubic feet in a stick of timber 33 
inches in diameter and 27 feet long ? 
Ans. 160.8688 cu. feet. 


Art. 329. What is a cone ? 


Jt isa solid figure witha circle at 
one end and gradually tapering to a 
point at the other end. 


Art. 330, To find the solidity of a cone, 


Rutz.— Multiply the area of the base by one-third of the 
altitude ; the product will be the solidity. 


103. What is the solidity of a cone whose base is 12 
feet in diameter and altitude 164 feet ? 
Ans. 622.0368 cu. feet. 


104. What is the solidity of a cone whose altitude is 
40 inches ard the base 105 inches in diameter ? 
Ans, 1154.538 cu. inches. 


MENSURATION. 267 


105. There is a stick of timber in the form of a cone; 
it is 28 feet long and 20 inches in diameter at one end, 
and gradually tapering to a point at the other end; what 
is the solidity of the cone ? Ans, 20.362 cu. feet. 


Art. 331. What is the frustrum 
of a cone 2 


It is that part of a cone which is 


left after a smaller cone ts cut of by =[|———-~ 
a plane parallel to the base. 


Art. 382, To find the solidity of the frustrurm of a 
cone, 


Ruir.—Add together the upper base, the lower base, and 
the mean proportional between the two bases ; multiply the 
sum thus found by one-third of the altitude of the frustrum, 
and the product will be the solidity. 


106. What 1s the solidity of the frustrum of a cone 
whose upper base contains 5 square feet, the lower base 
7 square feet, and the altitude 21 feet? 

Ans. 125.412 cu. ft. 


107. What is the solidity of the frustrum of a cone, 
the diameter of whose upper base is 28 inches, of the 
lower base 82 inches, and whose altitude is 10 feet ? 

Ans. 49.16 cu. ft. 


108. A stick of timber in the form of a conical frus- 
trum is 54 inches in circumference at the top, 64 inches 
at the bottom, and 9 feet high; what is its solidity ? 

Ans. 17.354 cu. ft. 


109. A caldron in the form of the fustrum of a cone 
is 4 feet in diameter at the top, 3 feet at the bottom, and 
4 feet deep; how many gallons will it hold ? 

Ans, 289,8433 gal. 


268 MENSURATION. 


Art. 833. What is a sphere ? 
A sphere or globe is a solid 
inclosed by a surface, every point 
of which is equally distant from 
a point within it, called the centre, 


Arr. 334. What is the diame- 
ter of a sphere ? 7 


It is a straight line drawn through the centre and 
terminated each way by the surface. 


Art. 335. What is the radius of a sphere ? 
It is a straight line drawn from the centre to the surface, 
Art. 336. To find the surface of a sphere, 


Rute.—find the area of a circle whose diameter is of 
the same length as the diameter of the sphere ; 4 times this 
area will be the area of the surface. 


110. What is the area of the surface of a sphere whose 


diameter is 48 feet ? Ans, 72388.2464 sq. ft. 
111. What is the area of the surface of a sphere whose 
radius is 75 yards ? Ans. 70686 sq. yd. 
112. What is the area of the surface of a sphere whose 
diameter is 163 inches ? Ans. 6 sq. ft. 82 sq. in. 
118. What is the area of the surface of a sphere whose 
radius is 89.44 rods ? Ans. 100524.9 sq. rd. 


114. How many square miles on the surface of the 
earth, counting the diameter 7912 miles? 
Ans. 196663355.7504 sq. m. 


115. How many square feet on the surface of a globe 
40 inches in circumference ? Ans. 509.294 sq. in. 


116. How many square yards on the surface of a bal] 
whose circumference is 100 fect ? 
| Ans. 3183.1 sq. ft. 


MENSURATION. 269 


117. What is the diameter of a sphere whose surface 
is 452 square feet ? Ans, 11.727 ft. 


118. Which contains the greater surface, a cube whose 
side is 20 feet, or a circle whose diameter is 20 feet ? 
Ans. 1143.86 sq. ft. more in the cube. 


Art. 337. To find the solidity of a sphere, 


Rure.—Multiply the surface of the sphere by one third 
of the radius. 


Art. 338. What is the ratio between two spheres of 
different dimensions ? 


They are to each other as the cubes of their radii or 
diameters. 


119. What is the solidity of a sphere 12 inches ir. 
diameter ? Ans, 904.7808 cu. in. 


120. What is the solidity of a globe 18 feet in diame- 
ter ? Ans. 8053.6352 cu. ft. 


121. What is the solidity of a sphere whose radius is 
51 feet ? Ans. 606.13245 cu. ft. 


122. What are the solid contents of a ball 4.5 inches 
in diameter ? Ans. 55.21845 cu. in. 


123. What is the solidity of a sphere whose circum- 
ference is 63 inches ? Ans, 7 cu. ft. 1169 cu. in. 


124. What is the solidity of a sphere whose surface is 
1440 square inches ? Ans. 2 cu. ft. 1680 cu. in. 


125. How much larger is a sphere 3 feet in diameter, 
than one 6 feet in diameter? Ans. 8 times as large. 


126. How many pounds in an iron ball 7 inches in 
diameter, supposing a cubic inch to weigh 2 of a pound? 
Ans. 67.34805 lb. 


27. How many bushels in a hemispherical bin, 4 feet 
in diameter, counting the U.S. measure of 2150.4 cubic 
inches to a bushel ? Ans. 13.463+ bu. 

23* 


Sal MISCELLANEOUS EXAMPLES, 
123. ‘There is a caldron in the shape of a hemisphere, _ 
© feet in diameter; how many bushels does it contain 
counting the New York measure of 2218.192 cubic 
inches to the bushel 2 Ans. 25.4-+ bu. 


129. What is the diameter of a sphere that contains 
2000 cubic inches 2 Ans. 15.63-+ in. 


130. What is the diameter of a hemisphere that con- 
tains 2 cubic feet ? Ans. Ans. 23.4-+ in. 


131. What is the diameter of a hemisphere that con- 
tains 100 gallons of wine, counting 231 cubic inches to 
the gallon ? Ans, 44.5 in. 


1382. How many times larger is a sphere 9 feet in 
diameter, than one 8 feet in diameter ? 
Ans, 27 times. 


133. If a cannon ball 24 inches in diameter weigh 3 
pounds, how many pounds will one weigh that is 10 
inches in diameter ? Ans, 192 lb. 


MISCELLANEOUS EXAMPLES. 


1, How many feet in 17 m. 3 fur, 21 rd. 24 yd. ? 
Ans. 92094 feet. 


2. Reduce 827 A. 1 R. 19 sq. p. 164 yd. to square 
feet. Ans. 142603314 sq. feet. 


3. Reduce 70 0000154 feet to degrees. 
Ans. 190 deg. 52 m. 4 fur, 25 rd. 1 yd. 


4, How many pints in 4 hhd. at measure as fol- 
.ows: the Ist, 62 gal. 3 qt. 1} pt. , the 2d, 61 gal. 1 qt. 
17 pt., the 3d, 59 gal. 3 qt. 13 pt., "and the 4th, 63 gal. ? 

Ans. 1979 pints. 


5. How many hours between the 15th of November, 
1851, at 7 P.M., and the 23d of March, 1852, at 5 
A. i 2 Ans. 3084 hours. 


. The latitude of Constantinople is 41° 0’ 12’; the 


MISCELLANEOUS EXAMPLES. Q71 


latitude of London is 51° 80’ 48’; how many statute 
miles is London north of Constantinople ? 2 
Ans. 730.445 miles. 


7. Take 18 T. 16 cwt. 1 qr. 15 Ib. 19 times, and di- 
ride the result by 5. Ans. 71 T. 10 cwt. 1 qr. 7 Ib. 


8. How many pounds N. York currency is $37.87) ? 
Ans. £15. 3s. 

9. How many pounds N. York currency is $98,683 2 
Ans. £35, 9s. 6d. 
10. Reduce $1843.78 to pounds N. York currency. 
Ans. £737 10s. 2.88d. 

11. Reduce $587.54 to pounds N. England currency. 
Ans. £176 5s. 2.88¢. 


12. How many pounds Virginia currency in $4811.54? 
Ans. £1443 9s. 2.88d. 


13. Add 4, 24, 34, and 12. Ans, 173, 
14, What is th m of = 24 “es 3 . 
s the sum + 74 9 ies oh 
ne 612, 
15. What is the difference between 174 and 34 ? 
* Ans, 131} . 
1 OL 
16. From 2 of 17? take 223, Ans. gly. 
50 150 
17. From 33+53 take 74. Ans, 1382. 
18. To the difference between 37 and thgad 61. 
5 ot. 
Ans. 63 
al 
19. From the difference betw een 5 and is take sok 
Ans. +3. 


20. There was a eorapany of soldiers, of whom 4 was 
on duty as sentinels, + was preparing dinner, and the 


OT MISCELLANEOUS EXAMPLES. 


rest, 19 men, were drilling; how many were there alto- 
gether ? Ans. 80 men. 


21. The sum of two numbers is 186.005, and the 
greater one is 93.0961; what is the smaller number ? 
Ans, 92.9089. 


22. If the difference of two numbers be 370,15, and 
the greater one 900, what will be the smaller ? 
Ans. 529.85. 
23. The sum of two numbers is 365, and their differ- 


ence is .0675 ; what are the numbers ? 
Ans, § 182-58875 and 
" ) 182.46625. 


24. The sum of two numbers is ? and their difference 
is 3; what are the two numbers? Ans. 2? and 


25. The product of two numbers is 1000, and one $8 


them is 31.25; what is the other ? Ans. 382, 
26. The product of two numbers is 3f, and one of them 
is $2; what is the other? Ans. 53. 


27. If the divisor to a certain number be 33.334 and 
the quotient 13, what will be the dividend ? 


Ans. 7d. 

28. What is the number, 2 of which is equal to 275 2? 
Ans. 330. 

29. ++4 of a certain number is ae Ai to 624; what 
is that number 2 Ans. ‘75. 


30. If from +3 of a number there be taken 4, the re- 
mainder will be ‘1612; ; What is that number ? 


Ans. 361, 


31. If A can do a piece of work in 15 days, and B can 
do the same in 25 days, how long would it take both, if 
they werk together ? Ans. 93 days. 

32. A and B can build a stone wallin 14 days; A ean 


do it alone in 21 days; how long would it take B to de 
it ? Ans. 42 days. 


MISCELLANEOUS EXAMPLES, Av 3 


33. If a barrel of flour will last one family 18 days, 
a second family 20 days, and a third 24 days, how long 
will it last the three families together ? 
Ans. 642, 


34. If 7 of a number be 60, what is the number ? 
Ans. 684, 


35. A person bought & of a vessel for $32000; what 
was the price of the whole ? Ans. $57600. 


36. If 2 of a steamboat be purchased by the captain, 
and he should sell 4 of his share for $500, what would 
be the valuation of the whole boat ? Ans. $3750. 


37. If a person buy 2 of a barrel of flour, and divide 
it into 6 equal parts, and sell each of these last parts for 
_ 45 cents, what would be the value of the barrel of flour ? 
Ans. $6.30. 


38. A merchant bought 2 of a coal mine, and after- 
ward purchased 34 of the mine, both of which cost him 
$8000 ; what is the valuation of the whole mine? 

Ans. $15238,7,. 


39. A person was going to buy 75 of a vessel, but he 
changed his mind and bought # of what he intended to 
buy, and paid $4900; what was the value of the whole ? 

Ans. $11200 


40, Abram Miller bought § of the ship Cleopatra; he 
kept + of what he bought, and sold the balance for 
$40000 ; what was the value of the whole vessel ? 


Ans. $56250. 


41, A stockbroker bought 2 of the capital of a com- 
pany at par; he sold 1 of his purchase at par and the 
rest for $25000; by the latter sale he made $5000; 


what was the value of the whole capital ? 
7 Ans. $36000. 


42. A capitalist purchased 4 of the capital of a bank 
at par; he retained 2 of his purchase and sold the bal- 


274. MISCELLANEOUS EXAMPLES. 


ance for $50000, thereby making 10 per cent. on the 
cost ; what was the total capital of the bank ? 
Ans. $90909.09. 


43. How many yards of carpet that is 3 yd. wide will 


cover a floor 25 feet by 40? Ans. 1484, yd. 
44. How long is a piece of ground that is 100 feet 
wide and contains 5 acres ? Ans. 2178 feet. 


45. A surveyor measured a piece of ground in the 
form of a rectangle, and found one side to be 87 chains, 
and the other 42 chains 16 links; how = —— did it 
contain ? Ans. 155 A. 3 RB. 38 sq. rd. 213% sq. yd. 


46. A farmer owns 425 acres of land which is in tne 
shape of a rectangle, one of the sides is 40 chains 15 links ; 
now long is the other side ? Ans. 105 ch. 85 links, 


47. How many building lots, each 50 feet by 100, can 
be made out of 24 acres of ground? Ans. 


48. A, B,.and C can build a barn in 10 days; after 4 
days A leaves, and B and C Boon ith the work for 5 
days longer, when B leaves, =°; of the work being yet 
unfinished ; C proceeds with the work and finishes it in 
114 days after B left; how long will it take to each 


builé the barn 2 A in 25 days. 
Ans.; Bin 30 “* 
Cin 872 “ 


49. Divide $600 between two persons, so that one 
shall have 2 as much as the other. 
Ans. $280 and $320. 


50. Divide $840 between A, B, and C, so that B shall 
have 2 of what A gets, and GC 2 as much as A and B 
together. A, $320. 

Ans. 4 B, $240. 
C, $280. 


51. How late is it when the time past noon is 4 of the 
time to midnight ? Ans. 20 minutes past 5. 


MISCELLANEOUS EXAMPLES. 275 


52. Divide $1560 between two persons, so that as 
often as one gets $7, the other shall get $5? 
Ans. $910 and $650. 


53. Divide $8145 between three persons, so that as. 
often as one gets $5, the second will get $6, and the 
third $7. $22622 for the Ist. 

Ans. 4 $2715 “ 2d, 
$31672 “ “ 3d. 


54, If two persons are engaged in business where one 
advances $550, and the other $450, and they gain $500, 
to how much is each entitled? Ans. $275 and $225. 

55. A, B, and C, commence business; A puts in 
$2250, B, $3'750, and C, $5000; they gain $1500; to 
hew much is each person entitled ? $187.50 for A. 

| Ans. + $562.50 for B. 
$750.00 for C. 

56. X and Y opened a grocery; X put in $1000, and 
Y 12 hhd. of sugar, each weighing 1250 lb., valued at 8 
cts. a pound, and 50 barrels of flour, at $7 a barrel ; they 
lost $200; what was the loss of each ? 

Ans. 

57. If the tire of a wheel is 10 ft. 3 in. in circum- 
ference, and the axle 54, ft. in diameter, how many times 
faster will the tire move than the axle ? 

Ans, 10+ times. 


58. Received from Rio Janeiro 300 bags of coffee, 
each bag 78 Ib., tare 54 per cent., and invoiced at 9 
cents a pound; for how much a pound should it be sold 
to gain 331 per cent., and what would be the total profit ? 

ee 12 cts. a pound. 
" | $663.39 total profit. 

59. Transferred from Boston to New York 1000 
yards of muslin, at 9d. a yard New England currency ; 
what is the price a yard, New York currency, and how 
much }ederal money must be sent to Boston to pay for 
the muslin ? pa 12d. New York currency a yard. 

" {| $125 must be sent to Boston. 


276 MISCELLANEOUS EXAMPLES. 


60. Received from Charleston 150 bales of cotton, 
each bale 600 pounds, and invoiced at 7d. a pound, 
South Carolina currency. It was sold at an advance 
of 25 per cent., commission 1 per cent. How much 
Federal money should be sent to Charleston to pay the 
owner ? Ans. $13921.875. 


(61.) 
New York, Jan. 1st, 1854. 
$500. 


Sixty days after date, I promise to pay to the order 
of James Brown five hundred dollars, value received. 
JosEPH ‘THOMPSON. 


The above note not being paid at maturity, was 
protested for non-payment. On the Ist of April the 
note was paid with interest at, '7 per cent. per annum, 
together with $2 for protest. How much was paid, 
counting 365 days to the year ? Ans. $504.59. 


(62.) 


Joseph Benson of Charleston, in account with Wilson 
G. Hunt of New York, 


Dr. 
JAnMtl, ood... LO cist, =. cee - « « $1000.00 
PLOW ae “ 250 yd. of cloth at $5 . 1250.00 
Peper ee Talti.’ wc Wr dees tae ees 500.00 


Cr. 


March Ist, By cash .arcii<) Guus dae eee 
May lat, cucf, ot6 wid... 8 eee mh © 1000.00 


What was the balance with interest at '7 per cent. per 
annum, on the Ist of July, 18538, counting by days, and 
365 days to the year ? 


Norz.—In this sum find the amount of each purchase and payment, from 
their dates to July Ist, 1853, and subtract the less sum from the greater, and 
whichever party has the greater amount, to him will the balance be due. 


Ans. $292.09 due W. G. H. 


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| DAVIES’ NEW PRIMARY ARITHMETIC. 

D/TIRS’ NEW INTELLECIVAL ARITHMETIC,” 
DAVIES’ ELEMENTS OF WRITTEN ARITHMETIC, 
| DAVIES’ NEW PRACTICAL ARITHMETIC, | a 
DAVIES’ NEW UNIVERSITY ARITHMETIC. | || | 


PRIMARY ARITHMETIC. This work is constructed on ite’ 
| principle -of object teaching. The combinations of numbe” 5 
are illustrated by sensible objects. The mind of the pupil is} i 
gradacliy Jed, by a series. of illustrations, from what is visible 
i and tangible, te the abstract properties of numbers, This work! a: 
is a specimen, in method, arrangement, style, and typography, 
| of the new series. ; 

NEW INTELLECTUAL ARITHMETIC, This work is eget: AL a 
| ed on the principle, that: svery operation in Arithmetic has. vet Pee 
erence to the unit 1. The whole subject is treated with reference % 
to this fact. The work differs essentially from the one which?) 7 
preceded it. It is, indeed, a new development of the subject, ~~ 4 
is confidently commended to the notice of teachers. 


ELEMENTS GF WRITTEN ARITHMETIC. This is a new work, 
designed as a Practical Introduction to the study of Arithme i 
It explains the operations of Arithmetic by Practical alae. | : 
carefully selected and graded. It embraces the five fondamet ™}} 
tal rules, Common and Decimal Fractions, and Depomihayy Bie 
Numbers. 

PRACTICAL ARITHMETIC. This work is a carefully teviselt : 
and improved edition « «>.» New Sehool Arithmetic, Many | 
changes were found nec sary, in the old work, to bring it into || | 
harmony with the othe. ,urts of the New Series. It vag | af 


? si 


therefore, deemed best to remodel it, and to give to it a ne 
ame—that it might not be confounded with previous onion 

aad that it might share in the many re which havé 

been introduced into the New Series. a 
UNIVERSITY ARITHMETIC. The object of this work is to teach 

| thé general principles and science of Numbers, and also to extend 

| their applications, not to change the method of‘application—these 

are, and  iahaamiiel et be PO ee same. 


